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

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

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

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

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derivative of

y = 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 x^{7} x^{4} + 2 d x

\frac{1}{x + 5}

y = 34 (3 x + 1)^{- \frac{2}{5}}

x \to - 1 lim (x^{4})

\frac{d}{d x} (ln ∣ 1 + x ∣)

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