Using the chain rule within product rule problems

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

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

Differentiation of  polynomials, cos, sin, exp, log functions. Product, quotient and chain rules.

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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 $g(x)$.

Differentiate

\[ \sqrt{a x^m+b})\]

This question applies a rewriting rule to the student's answer and correct answer, to interpret chained inequalities $a<b<c$ and $a>b>c$ as $(a<b) \wedge (b<c)$ and $(a>b) \wedge (b>c)$ respectively.

This is a work-around until the parser interprets chained relations this way automatically.

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

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

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 $g(x)$.

Examples on differentiation using the quotient rule and chain rule.

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

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

Differentiate

\[ \sqrt{a x^m+b})\]

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

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 $g(x)$.

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

Contains a video solving a similar example.

Chain rule

Use the chain rule to differentiate various functions.

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

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

Differentiation of  polynomials, cos, sin, exp, log functions. Product, quotient and chain rules.

From mathcentre.ac.uk