163 results for "differentiate".

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• Question in Demos

Contains some extremely basic code to do symbolic differentiation: it can give the derivative of terms of the form $x^n$, $sin(x)$ and $cos(x)$, and apply the chain rule.

• Question

Differentiate the function $f(x)=(a + b x)^m e ^ {n x}$ using the product rule. Find $g(x)$ such that $f\;'(x)= (a + b x)^{m-1} e ^ {n x}g(x)$.

• Question

Differentiate the function $(a + b x)^m e ^ {n x}$ using the product rule.

• Question

Differentiate $f(x)=x^{m}\sin(ax+b) e^{nx}$.

The answer is of the form:
$\displaystyle \frac{df}{dx}= x^{m-1}e^{nx}g(x)$ for a function $g(x)$.

Find $g(x)$.

• Question

Differentiate $(a+bx) ^ {m} \sin(nx)$

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Differentiate the following functions: $\displaystyle x ^ n \sinh(ax + b),\;\tanh(cx+d),\;\ln(\cosh(px+q))$

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Differentiate the following functions: $\displaystyle x ^ n \sinh(ax + b),\;\tanh(cx+d),\;\ln(\cosh(px+q))$

• Question

The derivative of $\displaystyle \frac{a+be^{cx}}{b+ae^{cx}}$ is $\displaystyle \frac{pe^{cx}} {(b+ae^{cx})^2}$. Find $p$.

• Question

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

• Question

The derivative of  $\displaystyle \frac{ax+b}{\sqrt{cx+d}}$ is $\displaystyle \frac{g(x)}{2(cx+d)^{3/2}}$. Find $g(x)$.

• Question

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

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Other method. Find $p,\;q$ such that $\displaystyle \frac{ax+b}{cx+d}= p+ \frac{q}{cx+d}$. Find the derivative of $\displaystyle \frac{ax+b}{cx+d}$.

• Question

Find $\displaystyle \frac{d}{dx}\left(\frac{m\sin(ax)+n\cos(ax)}{b\sin(ax)+c\cos(ax)}\right)$. Three part question.

• Exam (9 questions)

Use the quotient rule to differentiate various functions.

• Question

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

• Question

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

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

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Differentiate the function $f(x)=(a + b x)^m e ^ {n x}$ using the product rule. Find $g(x)$ such that $f^{\prime}(x)= (a + b x)^{m-1} e ^ {n x}g(x)$.

• Question

Differentiate $f(x) = (a x + b)/ \sqrt{c x + d}$ and find $g(x)$ such that $f^{\prime}(x) = g(x)/ (2(c x + d)^{3/2})$.

• Question

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

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

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Differentiate $\displaystyle e^{ax^{m} +bx^2+c}$

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Differentiate the following functions: $\displaystyle x ^ n \sinh(ax + b),\;\tanh(cx+d),\;\ln(\cosh(px+q))$

• Question

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

• Question

Differentiate $\displaystyle (ax^m+bx^2+c)^{n}$.

• Question

Differentiate

$\sqrt{a x^m+b})$

• Question

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

• Exam (8 questions)

Use the chain rule to differentiate various functions.

• Exam (11 questions)

Use the product rule to differentiate various functions.

• Question

Differentiate between linear and quadratic sequences and arithmetic and geometric sequences through a series of multiple choice questions. Spot different patterns in sequences like the triangle sequence, square sequence and cubic sequence and then use this pattern to find the next three terms in each of the sequences.