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Popular >

derivative of y=2xe^{2x}-e^{2x}

Solution

derivative of

y = 2 x e^{2 x} - e^{2 x}

Solution

4 e^{2 x} x

Solution steps

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

Apply the Sum/Difference Rule:

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

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

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

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

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

Simplify

2 (e^{2 x} + 2 e^{2 x} x) - e^{2 x} \cdot 2 : 4 e^{2 x} x

= 4 e^{2 x} x

Popular Examples

integral of 18sin^{-3/2}(x)cos^3(x)

\int 18 sin^{- \frac{3}{2}} (x) cos^{3} (x) d x

(x-8y)dx+(4x)dy=0

(x - 8 y) d x + (4 x) d y = 0

inverse oflaplace ((s+1)^3)/(s^5)inverse laplace

\frac{( s + 1 ) ^{3}}{s ^{5}}

limit as x approaches 5 of ((x-5))/(sqrt(x^2+5))

x \to 5 lim (\frac{( x - 5 )}{x ^{2} + 5})

integral from 0 to infinity of 4sin^2(a)

\int_{0}^{\infty} 4 sin^{2} (a) d a

Frequently Asked Questions (FAQ)

What is the derivative of y=2xe^{2x}-e^{2x} ?
The derivative of y=2xe^{2x}-e^{2x} is 4e^{2x}x
What is the first derivative of y=2xe^{2x}-e^{2x} ?
The first derivative of y=2xe^{2x}-e^{2x} is 4e^{2x}x