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

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Answer 1 · 2018-07-28T17:41:55

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

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}}#