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

The derivative of cos^7(x) is -7cos^6(x)sin(x)

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

The first derivative of cos^7(x) is -7cos^6(x)sin(x)

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\frac{d}{d x} (cos^{7} (x))

- 7 cos^{6} (x) sin (x)

Solution steps

\frac{d}{d x} (cos^{7} (x))

Apply the chain rule:

7 (cos (x))^{6} \frac{d}{d x} (cos (x))

= 7 (cos (x))^{6} \frac{d}{d x} (cos (x))

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

= 7 (cos (x))^{6} (- sin (x))

Simplify

= - 7 cos^{6} (x) sin (x)

y^{^{'}} = \frac{x ^{2} y + y ^{3}}{x ^{3}}

\frac{\partial}{\partial y} (- sin (y))

\int (1 - \frac{x}{a})^{3} d x

y^{^{''}} + 20 y^{^{'}} + y = 12

x \to 0 lim (3 + x^{2} sin (\frac{1}{x}))

What is the derivative of cos^7(x) ?
The derivative of cos^7(x) is -7cos^6(x)sin(x)
What is the first derivative of cos^7(x) ?
The first derivative of cos^7(x) is -7cos^6(x)sin(x)