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Popular >

derivative of arctan(5cos(x))

Solution

\frac{d}{d x} (arctan (5 cos (x)))

Solution

- \frac{5 sin ( x )}{25 cos ^{2} ( x ) + 1}

Solution steps

\frac{d}{d x} (arctan (5 cos (x)))

Apply the chain rule:

\frac{1}{( 5 cos ( x ) ) ^{2} + 1} \frac{d}{d x} (5 cos (x))

= \frac{1}{( 5 cos ( x ) ) ^{2} + 1} \frac{d}{d x} (5 cos (x))

\frac{d}{d x} (5 cos (x)) = - 5 sin (x)

= \frac{1}{( 5 cos ( x ) ) ^{2} + 1} (- 5 sin (x))

Simplify

\frac{1}{( 5 cos ( x ) ) ^{2} + 1} (- 5 sin (x)) : - \frac{5 sin ( x )}{25 cos ^{2} ( x ) + 1}

= - \frac{5 sin ( x )}{25 cos ^{2} ( x ) + 1}

Graph

Popular Examples

sum from k=1 to infinity of 1/(4^k)

k = 1 \sum \infty \frac{1}{4 ^{k}}

taylor sqrt(1+x^2)taylor

1 + x^{2}

tangent of f(x)=5x^2,\at x=-2 tangent of

f (x) = 5 x^{2}, at x = - 2

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y = t (ln (4 t))^{2}

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h \to 0 lim (\frac{2 ( x + h ) - 2 x}{h})

Frequently Asked Questions (FAQ)

What is the derivative of arctan(5cos(x)) ?
The derivative of arctan(5cos(x)) is -(5sin(x))/(25cos^2(x)+1)
What is the first derivative of arctan(5cos(x)) ?
The first derivative of arctan(5cos(x)) is -(5sin(x))/(25cos^2(x)+1)