Question

Asked Mar 13, 2019

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Determine f '(x) for f (x)=(3x^{2}+1)^{2}

Step 1

It is known that the chain rule is a formula for computing the derivative of the composition of two or more functions.

If *g* is differentiable at *x* and *f* is differentiable at *g*(*x*), then the composite function *F*(*x)* is differentiable at *x* and *F’* is given by the product *F’*(*x*)=*f*’(*g*(*x*))·*g\'*(*x*).

In Leibniz notation, If *y*=*f*(*u*) and *u*=*g*(*x*) are both differentiable functions, then

Step 2

Let *u*=3*x²*+1 and apply chain ru...

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