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Popular >

derivative of 3e^{2x}+2e^{2x}x

Solution

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

Solution

4 e^{2 x} x + 8 e^{2 x}

Solution steps

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

Apply the Sum/Difference Rule:

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

= \frac{d}{d x} (3 e^{2 x}) + \frac{d}{d x} (2 e^{2 x} x)

\frac{d}{d x} (3 e^{2 x}) = 6 e^{2 x}

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

= 6 e^{2 x} + 2 (2 e^{2 x} x + e^{2 x})

Simplify

6 e^{2 x} + 2 (2 e^{2 x} x + e^{2 x}) : 4 e^{2 x} x + 8 e^{2 x}

= 4 e^{2 x} x + 8 e^{2 x}

Popular Examples

tangent of f(x)=x^2+7,16,\at x=3 tangent of

f (x) = x^{2} + 7, 16, at x = 3

integral of (e^{-3t})/t

\int \frac{e ^{- 3 t}}{t} d t

derivative of 1/3 (3-5x)^3 derivative of

\frac{1}{3} (3 - 5 x)^{3}

y y^{^{'}} + 4 x = 0

limit as x approaches 2 of (x^3+8)/(x+2)

x \to 2 lim (\frac{x ^{3} + 8}{x + 2})

Frequently Asked Questions (FAQ)

What is the derivative of 3e^{2x}+2e^{2x}x ?
The derivative of 3e^{2x}+2e^{2x}x is 4e^{2x}x+8e^{2x}
What is the first derivative of 3e^{2x}+2e^{2x}x ?
The first derivative of 3e^{2x}+2e^{2x}x is 4e^{2x}x+8e^{2x}