Question

differentiation of -3T^2/2+36T+2​

Answer 1

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Calculus

Find the Derivative - d/dx square root of 36+x^2

√36+x236+x2

Use n√ax=axnaxn=axn to rewrite √36+x236+x2 as (36+x2)12(36+x2)12.

ddx[(36+x2)12]ddx[(36+x2)12]

Differentiate using the chain rule, which states that ddx[f(g(x))]ddx[f(g(x))] is f'(g(x))g'(x)f′(g(x))g′(x) where f(x)=x12f(x)=x12 and g(x)=36+x2g(x)=36+x2.

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12(36+x2)12−1ddx[36+x2]12(36+x2)12-1ddx[36+x2]

To write −1-1 as a fraction with a common denominator, multiplyby 2222.

12(36+x2)12−1⋅22ddx[36+x2]12(36+x2)12-1⋅22ddx[36+x2]

Combine −