What is the derivative of sin^{-2}(x^2+x) ?

The derivative of sin^{-2}(x^2+x) is -(2cos(x^2+x)(2x+1))/(sin^3(x^2+x))

What is the first derivative of sin^{-2}(x^2+x) ?

The first derivative of sin^{-2}(x^2+x) is -(2cos(x^2+x)(2x+1))/(sin^3(x^2+x))

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

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

Solution steps

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

Apply the chain rule:

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

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

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

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

Multiply fractions:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

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

\int 3 e^{5 x} - 3 cos (4 x) d x

x \to 0 lim (- (ln (x)))

t \to 0 lim (\frac{e ^{3 t} - 1}{t})

x \to \infty + lim (\frac{1}{x} + 4)

\frac{d}{d x} (\frac{6}{x - 1})

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