Question

Please explain the steps you would take to solve this derivative (gr 12 calc)

Answer 1

First step, derivative of the constant:

`f^(\prime)(x)=(1)/(2)(d(e^(-3x^2+tan(3x+5))))/(dx)`

Second step, the chain rule:

`\begin{gathered} =(1)/(2)e^(-3x^2+tan(3x+5))*(d(-3x^2+tan(3x+5)))/(dx) \\ =(1)/(2)e^(-3x^2+tan(3x+5))*\frac{(-6x+sec^2(3x+5)*3)}{} \end{gathered}`

Where we applied that the derivative of tangent is the secant^2.

Hence the answer is:

`(1)/(2)e^(-3x^2+tan(3x+5))*\frac{(-6x+3sec^2(3x+5))}{}`