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

The derivative of sin^3(cos(7x^2)) is -42xsin^2(cos(7x^2))cos(cos(7x^2))sin(7x^2)

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

The first derivative of sin^3(cos(7x^2)) is -42xsin^2(cos(7x^2))cos(cos(7x^2))sin(7x^2)

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

- 42 x sin^{2} (cos (7 x^{2})) cos (cos (7 x^{2})) sin (7 x^{2})

Solution steps

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

Apply the chain rule:

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

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

\frac{d}{d x} (sin (cos (7 x^{2}))) = - 14 x cos (cos (7 x^{2})) sin (7 x^{2})

= 3 (sin (cos (7 x^{2})))^{2} (- 14 x cos (cos (7 x^{2})) sin (7 x^{2}))

Simplify

= - 42 x sin^{2} (cos (7 x^{2})) cos (cos (7 x^{2})) sin (7 x^{2})

\int \frac{1}{4 sin ^{2} ( x )} d x

\frac{d y}{d t} - 2 y = 3 e^{t}

\int sin^{2} (5 x) cos^{4} (5 x) d x

\int_{- 3}^{3} 9 x^{2} d x

y^{^{''}} - 6 y^{^{'}} + 9 y = 6 x^{2} e^{3 x}

What is the derivative of sin^3(cos(7x^2)) ?
The derivative of sin^3(cos(7x^2)) is -42xsin^2(cos(7x^2))cos(cos(7x^2))sin(7x^2)
What is the first derivative of sin^3(cos(7x^2)) ?
The first derivative of sin^3(cos(7x^2)) is -42xsin^2(cos(7x^2))cos(cos(7x^2))sin(7x^2)