What is the derivative of ln((x^2(x^3+1))/(e^{2x)}) ?

The derivative of ln((x^2(x^3+1))/(e^{2x)}) is (5x^3+2)/(x(x^3+1))-2

What is the first derivative of ln((x^2(x^3+1))/(e^{2x)}) ?

The first derivative of ln((x^2(x^3+1))/(e^{2x)}) is (5x^3+2)/(x(x^3+1))-2

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derivative of

ln (\frac{x ^{2} ( x ^{3} + 1 )}{e ^{2 x}})

\frac{5 x ^{3} + 2}{x ( x ^{3} + 1 )} - 2

Solution steps

\frac{d}{d x} (ln (\frac{x ^{2} ( x ^{3} + 1 )}{e ^{2 x}}))

Simplify

ln (\frac{x ^{2} ( x ^{3} + 1 )}{e ^{2 x}}) : ln (x^{2} (x^{3} + 1)) - 2 x

= \frac{d}{d x} (ln (x^{2} (x^{3} + 1)) - 2 x)

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{d}{d x} (ln (x^{2} (x^{3} + 1))) - \frac{d}{d x} (2 x)

\frac{d}{d x} (ln (x^{2} (x^{3} + 1))) = \frac{5 x ^{3} + 2}{x ( x ^{3} + 1 )}

\frac{d}{d x} (2 x) = 2

= \frac{5 x ^{3} + 2}{x ( x ^{3} + 1 )} - 2

\frac{d}{d x} (4 + x - 7)

\frac{x ^{2} - 3 x}{x + 1}

\int (2 x^{- 3} + x^{- \frac{1}{2}}) d x

\int csc (8 x) d x

\int (5 e^{- x} - \frac{3}{2})^{2} d x

What is the derivative of ln((x^2(x^3+1))/(e^{2x)}) ?
The derivative of ln((x^2(x^3+1))/(e^{2x)}) is (5x^3+2)/(x(x^3+1))-2
What is the first derivative of ln((x^2(x^3+1))/(e^{2x)}) ?
The first derivative of ln((x^2(x^3+1))/(e^{2x)}) is (5x^3+2)/(x(x^3+1))-2