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Popular >

derivative of e^x-1+e^xx

Solution

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

Solution

e^{x} x + 2 e^{x}

Solution steps

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

Apply the Sum/Difference Rule:

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

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

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

\frac{d}{d x} (1) = 0

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

= e^{x} - 0 + e^{x} x + e^{x}

Simplify

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

Popular Examples

(\partial)/(\partial x)(x^{0.2}y^{0.8})

\frac{\partial}{\partial x} (x^{0.2} y^{0.8})

integral of (4x+3)(2x^2+3)^3

\int (4 x + 3) (2 x^{2} + 3)^{3} d x

(\partial)/(\partial z)(x^2y^3z)

\frac{\partial}{\partial z} (x^{2} y^{3} z)

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

\frac{d}{d x} (\frac{1}{2 + x})

(dy)/(dx)=2-(2x)/(1000-x)

\frac{d y}{d x} = 2 - \frac{2 x}{1000 - x}

Frequently Asked Questions (FAQ)

What is the derivative of e^x-1+e^xx ?
The derivative of e^x-1+e^xx is e^xx+2e^x
What is the first derivative of e^x-1+e^xx ?
The first derivative of e^x-1+e^xx is e^xx+2e^x