Using differentiation to find the tangent and normal to a line at a given point

More work on differentiation with trigonometric functions

Differentiate $x^m\cos(ax+b)$

Differentiate $\displaystyle ax^b, ax^b+cx^{1/d}, \frac{a}{x^{1/c}}+\frac{b}{x^{-1/d}}+c$ with respect to $x$.

Find the gradient of  $ \displaystyle ax^b+\frac{c}{x^{d}}+f$ at $x=a$

Find the stationary points of a cubic which has 2 turning points.

Examples on differentiation using the quotient rule and chain rule.

Standard derivatives asked for (e.g. $x^n$, $1/x^n$, $\sqrt(x)$, $\ln(x)$, $\sin(x)$, etc.) .  

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For ENG1002 - Matlab Lab 4: Differentiation, Integration, Solving Differentiation equations.

For ENG1002 - Matlab Lab 4: Differentiation, Integration, Solving Differentiation equations.

For ENG1002 - Matlab Lab 4: Differentiation, Integration, Solving Differentiation equations.

A quadratic is and a graph of it is given. A tangent is also sketched. The equation of the tangent line is asked for.

A basic introduction to differentiation

A question to test basic differentiation of functions, including powers of x, trig, log and exponential functions.

A quadratic is and a graph of it is given. A tangent is also sketch. The equation of the tangent line is asked for.

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More work on differentiation with trigonometric functions

Chain rule

Implicit differentiation.

Given $x^2+y^2+ax+by=c$ find $\displaystyle \frac{dy}{dx}$ in terms of $x$ and $y$.

Find $\frac{\mathrm{d}y}{\mathrm{d}x}$ by differentiating an implicit equation.

Differentiate $f(x) = x^m(a x+b)^n$.

Differentiate $x^m\cos(ax+b)$

Differentiate $ \sin(ax+b) e ^ {nx}$.

Differentiate $\displaystyle \frac{ax+b}{cx+d}$.

The derivative of $\displaystyle \frac{ax+b}{cx^2+d}$ is of the form $\displaystyle \frac{g(x)}{(cx^2+d)^2}$. Find $g(x)$.

Use the quotient rule to differentiate various functions.

Questions on differentiation from first principles, and continuity and differentiability.

Use the chain rule to differentiate various functions.