What is the derivative of sin^n(x) ?

The derivative of sin^n(x) is ncos(x)sin^{n-1}(x)

What is the first derivative of sin^n(x) ?

The first derivative of sin^n(x) is ncos(x)sin^{n-1}(x)

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\frac{d}{d x} (sin^{n} (x))

n cos (x) sin^{n - 1} (x)

Solution steps

\frac{d}{d x} (sin^{n} (x))

Apply the chain rule:

n (sin (x))^{n - 1} \frac{d}{d x} (sin (x))

= n (sin (x))^{n - 1} \frac{d}{d x} (sin (x))

\frac{d}{d x} (sin (x)) = cos (x)

= n (sin (x))^{n - 1} cos (x)

Simplify

= n cos (x) sin^{n - 1} (x)

\frac{d}{d x} (ln (\frac{( x - 1 )}{x + 1}))

4 x y^{3} y^{^{'}} = x^{4} + 4 y^{4}

\int 49 - x^{2} d x

\int \frac{x ^{5} - x ^{3} + 8 x}{x ^{4}} d x

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

What is the derivative of sin^n(x) ?
The derivative of sin^n(x) is ncos(x)sin^{n-1}(x)
What is the first derivative of sin^n(x) ?
The first derivative of sin^n(x) is ncos(x)sin^{n-1}(x)