Question

d/dx(e^x^3)
help me out.
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Answer 1

Answer:

$\frac{d}{dx}( {e}^{ {x}^{3}})= 3 {e}^{ {x}^{3} } {x}^{2}$

Explanation:

$Here, y=e^{x^{3}} \\ Let, x^3 =u ..........(1)\\ \therefore y= e^u \\ Now, we \: know \: that,\\ \frac{d(e^x)}{dx}=e^x \\ \therefore \frac{dy}{du} = {e}^{u} ..........(2) \\ Now, In Eq(1),\\ x^3=u \\ \therefore \frac{du}{dx}=3x^{3 - 1} \\ \therefore \frac{du}{dx} = 3 {x}^{2} ..........(3) \\ Now, Multiplying \: Eq(2) \: by \: Eq(3), \\ \therefore \frac{dy}{du} \times \frac{du}{dx} = {e}^{u} \times 3 {x}^{2} \\ Now, putting \: value \: of \: x \: from \: Eq(1), \\ \therefore \frac{dy}{dx} = 3 {e}^{ {x}^{3} } {x}^{2}$