Question

If f(x)=3x3−2 and g(x)=e2x, what is f'(g(x))?

Answer 1

Answer:

$f^I(g(x))=9e^{4x}$

Step-by-step explanation:

$f(x)=3x^3-2\\\\g(x)=e^{2x}\\\\now\\\\f^I(x)=9x^2\\\\g^I(x)=2e^{2x}\\\\fog(x)=3(e^{2x})^3-2\\\\f(g(x))=3e^{6x}-2\\\\Differentiate \;w.r.t.\;x\\\\f^I(g(x))g^I(x)=18e^{6x}\\\\f^I(g(x))=\frac{18e^{6x}}{g^I(x)}\\\\f^I(g(x))=9e^{4x}$$f^I(g(x))=9e^{4x}$$f^I(g(x))=9e^{4x}$$f^I(g(x))=9e^{4x}$

HOPE IT HELPS.