Calculus I Assignment # 5

This assignment covers
Exponential and Log Derivatives
Logarithmic Differentiation

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QUESTIONS

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Find the derivative

 1) 2) 3) 4) 5) y = x ln x 6) y = 5 3x + (3x) 5. 7) 8) y = (x² + 1) 2x . 9) y = x² e - cot 2x . 10) y = x sin 5x

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SOLUTIONS

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Find the derivative

 1) Rewrite f (x) using log rules 2) Rewrite f (x) using log rules 3) so y' = 2x 4) Rewrite f (x) using log rules 5) use logarithmic differentiation it's a variable to a variable exponent.now, y = x ln x t ln y = (ln x) 2 or ln 2 x. 6) y' = 3(5 3x) ln 5 + 15(3x) 4. 7) 8) use logarithmic differentiation it's a variable to a variable exponent. ln y = 2x ln (x² + 1) so so 9) we use product rule here y' = 2x e - cot 2x + 2x² csc² 2x e - cot 2x .with some factoring, y' = 2x e - cot 2x (1 + x csc² 2x) . 10) use logarithmic differentiation it's a variable to a variable exponent. ln y = sin 5x (ln x)Using product rule again we get so

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