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Popular >

derivative of e^{ax}+arctan(cx)

Solution

\frac{d}{d x} (e^{a x} + arctan (c x))

Solution

e^{a x} a + \frac{c}{c ^{2} x ^{2} + 1}

Solution steps

\frac{d}{d x} (e^{a x} + arctan (c x))

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{d}{d x} (e^{a x}) + \frac{d}{d x} (arctan (c x))

\frac{d}{d x} (e^{a x}) = e^{a x} a

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

= e^{a x} a + \frac{c}{c ^{2} x ^{2} + 1}

Popular Examples

derivative of y= 7/(3x^4)derivative of

y = \frac{7}{3 x ^{4}}

integral of (x^3)/((a^2+x^2)^2)

\int \frac{x ^{3}}{( a ^{2} + x ^{2} ) ^{2}} d x

limit as x approaches-1-of (x^2)/(1+x^3)

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

integral from-2 to 4 of 1/2

\int_{- 2}^{4} \frac{1}{2} d x

derivative of e^{-2x}cos(4x)

\frac{d}{d x} (e^{- 2 x} cos (4 x))

Frequently Asked Questions (FAQ)

What is the derivative of e^{ax}+arctan(cx) ?
The derivative of e^{ax}+arctan(cx) is e^{ax}a+c/(c^2x^2+1)
What is the first derivative of e^{ax}+arctan(cx) ?
The first derivative of e^{ax}+arctan(cx) is e^{ax}a+c/(c^2x^2+1)