What is the derivative of ln(sin^3(x^2+7)) ?

The derivative of ln(sin^3(x^2+7)) is 6xcot(x^2+7)

What is the first derivative of ln(sin^3(x^2+7)) ?

The first derivative of ln(sin^3(x^2+7)) is 6xcot(x^2+7)

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\frac{d}{d x} (ln (sin^{3} (x^{2} + 7)))

6 x cot (x^{2} + 7)

Solution steps

\frac{d}{d x} (ln (sin^{3} (x^{2} + 7)))

Apply the chain rule:

\frac{1}{sin ^{3} ( x ^{2} + 7 )} \frac{d}{d x} (sin^{3} (x^{2} + 7))

= \frac{1}{sin ^{3} ( x ^{2} + 7 )} \frac{d}{d x} (sin^{3} (x^{2} + 7))

\frac{d}{d x} (sin^{3} (x^{2} + 7)) = 6 x sin^{2} (x^{2} + 7) cos (x^{2} + 7)

= \frac{1}{sin ^{3} ( x ^{2} + 7 )} \cdot 6 x sin^{2} (x^{2} + 7) cos (x^{2} + 7)

Simplify

\frac{1}{sin ^{3} ( x ^{2} + 7 )} \cdot 6 x sin^{2} (x^{2} + 7) cos (x^{2} + 7) : 6 x cot (x^{2} + 7)

= 6 x cot (x^{2} + 7)

y = tan^{2} (x)

y^{3} + x y^{2} - 61 = x + 3 y^{2}, at x = 3

\int \frac{x ^{2}}{2 - x} d x

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

\int cot (10 x) csc^{4} (10 z)

What is the derivative of ln(sin^3(x^2+7)) ?
The derivative of ln(sin^3(x^2+7)) is 6xcot(x^2+7)
What is the first derivative of ln(sin^3(x^2+7)) ?
The first derivative of ln(sin^3(x^2+7)) is 6xcot(x^2+7)