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Popular Calculus >

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}

Graph

Popular Examples

derivative of (x^6)/6+1/(16x^4)

d er i v a t i v e \frac{x ^{6}}{6} + \frac{1}{16 x ^{4}}

integral from 0 to 1 of 7x5^x

\int_{0}^{1} 7 x 5^{x} d x

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

d er i v a t i v e \frac{( 2 x + 1 )}{x + 2}

\frac{d}{d t} (2 t^{4})

integral of 3x^{1/2}

\int 3 x^{\frac{1}{2}} d x

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}