Question

How do you differentiate `f(x)=(4+e^(sqrt(7x)))^3` using the chain rule.?

Answer 1

`f'(x)=21/{2\sqrt{7x}}(4+e^{\sqrt{7x}})^2e^{\sqrt{7x}}`

Explanation:

Given function:

`f(x)=(4+e^{\sqrt{7x}})^3`

differentiating above equation w.r.t. `x` using chain rule as folows

`d/dxf(x)=d/dx(4+e^{\sqrt{7x}})^3`

`f'(x)=3(4+e^{\sqrt{7x}})^2d/dx(4+e^{\sqrt{7x}})`

`=3(4+e^{\sqrt{7x}})^2(0+e^{\sqrt{7x}}d/dx(\sqrt{7x}))`

`=3(4+e^{\sqrt{7x}})^2(e^{\sqrt{7x}}(1/{2\sqrt{7x}}d/dx(7x)))`

`=3(4+e^{\sqrt{7x}})^2({e^{\sqrt{7x}}}/{2\sqrt{7x}}(7)))`

`=21/{2\sqrt{7x}}(4+e^{\sqrt{7x}})^2e^{\sqrt{7x}}`