(y) = In(x^2) at the point where x

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(y) = In(x^2) at the point where x = e.

Answer & Explanation



Skilled2022-01-30Added 94 answers

Find the first derivative and evaluate at x=e and y=2 to find the slope of the tangent line.Differentiate using the chain rule, which states that ddx[f(g(x))] is f(g(x))g(x) where f(z)=lnx and g(x)=x2To apply the Chain Rule, set u as x2.ddu[ln(u)]ddx[x2]The derivative of ln(u) with respect to u is 1u.1uddx[x2]Replace all occurrences of u with x2.1x2ddx[x2]Differentiate using the Power Rule.Differentiate using the Power Rule which states that ddx[xn] is nxn1 where n=2.1x2(2x)Simplify terms.2xEvaluate the derivative at x=e2e

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