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Popular >

derivative of e^{2x}+sin(x^2)

Solution

\frac{d}{d x} (e^{2 x} + sin (x^{2}))

Solution

e^{2 x} \cdot 2 + cos (x^{2}) \cdot 2 x

Solution steps

\frac{d}{d x} (e^{2 x} + sin (x^{2}))

Apply the Sum/Difference Rule:

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

= \frac{d}{d x} (e^{2 x}) + \frac{d}{d x} (sin (x^{2}))

\frac{d}{d x} (e^{2 x}) = e^{2 x} \cdot 2

\frac{d}{d x} (sin (x^{2})) = cos (x^{2}) \cdot 2 x

= e^{2 x} \cdot 2 + cos (x^{2}) \cdot 2 x

Graph

Popular Examples

derivative of 4e^{3x}

\frac{d}{d x} (4 e^{3 x})

derivative of f(x)=(x^3+2x-2)^4 derivative of

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3 e^{3 x} \frac{d y}{d x} = - 9 \frac{x}{y ^{2}}

limit as x approaches pi/2 of 7sec(x)-7tan(x)

x \to \frac{π}{2} lim (7 sec (x) - 7 tan (x))

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\frac{d}{d x} (arctan (\frac{x - 1}{x + 1}))

Frequently Asked Questions (FAQ)

What is the derivative of e^{2x}+sin(x^2) ?
The derivative of e^{2x}+sin(x^2) is e^{2x}*2+cos(x^2)*2x
What is the first derivative of e^{2x}+sin(x^2) ?
The first derivative of e^{2x}+sin(x^2) is e^{2x}*2+cos(x^2)*2x