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Chain rule
Draft
Question in Bill's workspace by Bill Foster

Differentiate $\displaystyle \ln((ax+b)^{m})$
Chain rule
Draft
Question in Bill's workspace by Bill Foster

The derivative of $\displaystyle x ^ {m}(ax^2+b)^{n}$ is of the form $\displaystyle x^{m-1}(ax^2+b)^{n-1}g(x)$ . Find $g(x)$ .
Chain rule
Draft
Question in Bill's workspace by Bill Foster

Differentiate

$\sqrt{a x^m+b})$
Chain rule
Draft
Question in Bill's workspace by Bill Foster

Differentiate $\displaystyle e^{ax^{m} +bx^2+c}$
Chain rule
Draft
Question in Bill's workspace by Bill Foster

Differentiate the following functions: $\displaystyle x ^ n \sinh(ax + b),\;\tanh(cx+d),\;\ln(\cosh(px+q))$
Chain rule. (Video).
Draft
Question in Bill's workspace by Bill Foster

Differentiate $\displaystyle \cos(e^{ax}+bx^2+c)$ .

Contains a video solving a similar example.
Lois's copy of Basic differentiation 1
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Question in Calculus by Lois Rollings and 2 others

A question to test basic differentiation of functions, including powers of x, trig, log and exponential functions.
Use Green's theorem to convert line integral to double integral,
Ready to use
Question in Content created by Newcastle University by Newcastle University Mathematics and Statistics

(Green’s theorem). $\Gamma$ a rectangle, find: $\displaystyle \oint_{\Gamma} \left(ax^2-by \right)\;dx+\left(cy^2+px\right)\;dy$ .
Implicit differentiation
Draft
Question in Content created by Newcastle University by Newcastle University Mathematics and Statistics

Implicit differentiation.

Given $x^2+y^2+ax+by=c$ find $\displaystyle \frac{dy}{dx}$ in terms of $x$ and $y$ .
Differentiate product of trig function and binomial
Draft
Question in Content created by Newcastle University by Newcastle University Mathematics and Statistics

Differentiate $(a+bx) ^ {m} \sin(nx)$
Differentiate product of binomial and exponential
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Question in Content created by Newcastle University by Newcastle University Mathematics and Statistics

Differentiate the function $(a + b x)^m e ^ {n x}$ using the product rule.
Differentation: Product Rule
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Question in Content created by Newcastle University by Newcastle University Mathematics and Statistics

Differentiate the function $f(x)=(a + b x)^m e ^ {n x}$ using the product rule. Find $g(x)$ such that $f\;'(x)= (a + b x)^{m-1} e ^ {n x}g(x)$ .
Differentiate products of hyperbolic functions
Draft
Question in Content created by Newcastle University by Newcastle University Mathematics and Statistics

Differentiate the following functions: $\displaystyle x ^ n \sinh(ax + b),\;\tanh(cx+d),\;\ln(\cosh(px+q))$
Differentiate products of trig, log and exponential terms
Draft
Question in Content created by Newcastle University by Newcastle University Mathematics and Statistics

Differentiate the following functions: $\displaystyle x ^ n \sinh(ax + b),\;\tanh(cx+d),\;\ln(\cosh(px+q))$
Differentiation: Product rule
Draft
Question in Content created by Newcastle University by Newcastle University Mathematics and Statistics

Differentiate $f(x) = x^m(a x+b)^n$ .
Differentiation: Product rule
Draft
Question in Content created by Newcastle University by Newcastle University Mathematics and Statistics

Differentiate $x^m\cos(ax+b)$
Quotient rule - differentiate quotient of linear terms
Ready to use
Question in Content created by Newcastle University by Newcastle University Mathematics and Statistics

Other method. Find $p,\;q$ such that $\displaystyle \frac{ax+b}{cx+d}= p+ \frac{q}{cx+d}$ . Find the derivative of $\displaystyle \frac{ax+b}{cx+d}$ .
Differentiation: Quotient rule
Draft
Question in Content created by Newcastle University by Newcastle University Mathematics and Statistics

The derivative of $\displaystyle \frac{ax+b}{cx^2+d}$ is of the form $\displaystyle \frac{g(x)}{(cx^2+d)^2}$ . Find $g(x)$ .
Quotient rule - differentiate linear over quadratic
Ready to use
Question in Content created by Newcastle University by Newcastle University Mathematics and Statistics and 1 other

The derivative of $\displaystyle \frac{ax+b}{cx^2+dx+f}$ is $\displaystyle \frac{g(x)}{(cx^2+dx+f)^2}$ . Find $g(x)$ .
Differentiation: Product rule
Draft
Question in Content created by Newcastle University by Newcastle University Mathematics and Statistics

Differentiate $\sin(ax+b) e ^ {nx}$ .
Quotient rule - differentiate linear over square root
Ready to use
Question in Content created by Newcastle University by Newcastle University Mathematics and Statistics

The derivative of $\displaystyle \frac{ax+b}{\sqrt{cx+d}}$ is $\displaystyle \frac{g(x)}{2(cx+d)^{3/2}}$ . Find $g(x)$ .
Quotient rule - differentiate exponential over exponential
Ready to use
Question in Content created by Newcastle University by Newcastle University Mathematics and Statistics

The derivative of $\displaystyle \frac{a+be^{cx}}{b+ae^{cx}}$ is $\displaystyle \frac{pe^{cx}} {(b+ae^{cx})^2}$ . Find $p$ .
Differentiation: Quotient rule
Draft
Question in Content created by Newcastle University by Newcastle University Mathematics and Statistics

Differentiate $\displaystyle \frac{ax+b}{cx+d}$ .
Quotient rule - differentiate quadratic over quadratic
Ready to use
Question in Content created by Newcastle University by Newcastle University Mathematics and Statistics

The derivative of $\displaystyle \frac{ax^2+b}{cx^2+d}$ is $\displaystyle \frac{g(x)}{(cx^2+d)^2}$ . Find $g(x)$ .
Chain rule - hyperbolic and log functions
Draft
Question in Content created by Newcastle University by Newcastle University Mathematics and Statistics

Differentiate the following functions: $\displaystyle x ^ n \sinh(ax + b),\;\tanh(cx+d),\;\ln(\cosh(px+q))$
Chain rule - exponential of polynomial,
Draft
Question in Content created by Newcastle University by Newcastle University Mathematics and Statistics

Differentiate $\displaystyle e^{ax^{m} +bx^2+c}$
Function approximation
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Question in Content created by Newcastle University by Newcastle University Mathematics and Statistics

Approximate $f(x)=(a+h)^{m/n}$ by $f(a)+hf^{\prime}(a)$ to 5 decimal places and compare with true value.
Differential Equation Question Type
Draft
Question in Andrew's workspace by Andrew Iskauskas

Solving a second-order constant coefficient ODE. Uses the differentiation extension: https://github.com/Tandethsquire/Differentiation, and the Differential Equation custom part type, to differentiate a student answer and ensure it satisfies the equation.
Implicit Differentiation
Draft
Question in Clare Year 3 by Clare Lundon

Implicit differentiation.

Given $x^2+y^2+ax+by=c$ find $\displaystyle \frac{dy}{dx}$ in terms of $x$ and $y$ .
Lois's copy of Chain rule
Draft
Question in Calculus by Lois Rollings

Differentiate $\displaystyle (ax^m+b)^{n}$ .

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