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

The derivative of sin^{n-1}(x) is cos(x)sin^{n-2}(x)(n-1)

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

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

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

cos (x) sin^{n - 2} (x) (n - 1)

Solution steps

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

Apply the chain rule:

(sin (x))^{n - 2} (n - 1) \frac{d}{d x} (sin (x))

= (sin (x))^{n - 2} (n - 1) \frac{d}{d x} (sin (x))

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

= (sin (x))^{n - 2} (n - 1) cos (x)

Simplify

= cos (x) sin^{n - 2} (x) (n - 1)

f (x) = - \frac{3}{x ^{2} - 4}, (1, 1)

x \to 0 lim (x^{6} sin (\frac{6}{x}))

\frac{d y}{d t} = cos (t)

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

\int (\frac{1}{x \cdot ( 5 - x )}) d x

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