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Popular >

derivative of cos(arctan(5x))

Solution

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

Solution

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

Solution steps

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

Apply the chain rule:

- sin (arctan (5 x)) \frac{d}{d x} (arctan (5 x))

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

\frac{d}{d x} (arctan (5 x)) = \frac{5}{25 x ^{2} + 1}

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

Simplify

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

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

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n = 0 \sum \infty n^{n} (x - 3)^{n}

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x \to 2 lim (\frac{3}{x + 2})

inverse oflaplace s/((s-2)(s-3)(s-6))inverse laplace

\frac{s}{( s - 2 ) ( s - 3 ) ( s - 6 )}

derivative of ((x^2+1)/((x+4)))

\frac{d}{d x} (\frac{( x ^{2} + 1 )}{( x + 4 )})

derivative of y=(5x+1)^3(x-4)derivative of

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Frequently Asked Questions (FAQ)

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