What is the derivative of ln(x^3sin^2(x)) ?

The derivative of ln(x^3sin^2(x)) is (3sin^2(x)+xsin(2x))/(xsin^2(x))

What is the first derivative of ln(x^3sin^2(x)) ?

The first derivative of ln(x^3sin^2(x)) is (3sin^2(x)+xsin(2x))/(xsin^2(x))

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derivative of

ln (x^{3} sin^{2} (x))

\frac{3 sin ^{2} ( x ) + x sin ( 2 x )}{x sin ^{2} ( x )}

Solution steps

\frac{d}{d x} (ln (x^{3} sin^{2} (x)))

Apply the chain rule:

\frac{1}{x ^{3} sin ^{2} ( x )} \frac{d}{d x} (x^{3} sin^{2} (x))

= \frac{1}{x ^{3} sin ^{2} ( x )} \frac{d}{d x} (x^{3} sin^{2} (x))

\frac{d}{d x} (x^{3} sin^{2} (x)) = 3 x^{2} sin^{2} (x) + sin (2 x) x^{3}

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

Simplify

\frac{1}{x ^{3} sin ^{2} ( x )} (3 x^{2} sin^{2} (x) + sin (2 x) x^{3}) : \frac{3 sin ^{2} ( x ) + x sin ( 2 x )}{x sin ^{2} ( x )}

= \frac{3 sin ^{2} ( x ) + x sin ( 2 x )}{x sin ^{2} ( x )}

\int \frac{6 x ^{2} - 11 x + 5}{3 x - 1} d x

\int_{- \infty}^{2} \frac{2}{x ^{2} + 4} d x

f (x) = 2 x - x^{2}

\int cos (x) sin^{5} (x) d x

3 - x, - 4 \leq x \leq 2

What is the derivative of ln(x^3sin^2(x)) ?
The derivative of ln(x^3sin^2(x)) is (3sin^2(x)+xsin(2x))/(xsin^2(x))
What is the first derivative of ln(x^3sin^2(x)) ?
The first derivative of ln(x^3sin^2(x)) is (3sin^2(x)+xsin(2x))/(xsin^2(x))