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Popular >

derivative of c_{1}e^x+c_{2}xe^x

Solution

\frac{d}{d x} (c_{1} e^{x} + c_{2} x e^{x})

Solution

c_{1} e^{x} + c_{2} (e^{x} + e^{x} x)

Solution steps

\frac{d}{d x} (c_{1} e^{x} + c_{2} x e^{x})

Apply the Sum/Difference Rule:

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

= \frac{d}{d x} (c_{1} e^{x}) + \frac{d}{d x} (c_{2} x e^{x})

\frac{d}{d x} (c_{1} e^{x}) = c_{1} e^{x}

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

= c_{1} e^{x} + c_{2} (e^{x} + e^{x} x)

Popular Examples

sum from n=0 to infinity of 1/(10^n)

n = 0 \sum \infty \frac{1}{1 0 ^{n}}

y^'+7y=t+e^{-2t}

y^{^{'}} + 7 y = t + e^{- 2 t}

limit as x approaches 0+of x^3+3x+2

x \to 0 + lim (x^{3} + 3 x + 2)

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

\int \frac{2}{x ^{2} + 2 x + 2} d x

limit as x approaches 1-of x^2-1

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

Frequently Asked Questions (FAQ)

What is the derivative of c_{1}e^x+c_{2}xe^x ?
The derivative of c_{1}e^x+c_{2}xe^x is c_{1}e^x+c_{2}(e^x+e^xx)
What is the first derivative of c_{1}e^x+c_{2}xe^x ?
The first derivative of c_{1}e^x+c_{2}xe^x is c_{1}e^x+c_{2}(e^x+e^xx)