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

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

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

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

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

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

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

y = x^{4} - 4 x^{3} + 10

2 x, x ∣ x + 2 ∣

\frac{d y}{d x} + 3 y = 10, y (0) = 20

x y = 24, 2 x^{2} - y^{2} + 4 = 0

\frac{d y}{d x} = \frac{x ^{2}}{10 y} - \frac{2 x}{5 y}

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