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Popular >

derivative of (x^2+1e^{x-1})

Solution

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

Solution

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

Solution steps

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

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = x^{2} + 1, g = e^{x - 1}

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

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

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

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

Popular Examples

y^{''}+3y^'=0,y(0)=7,y^'(0)=-3

y^{^{''}} + 3 y^{^{'}} = 0, y (0) = 7, y^{^{'}} (0) = - 3

x(dy)/(dx)+(3x+1)y=e^{-3x}

x \frac{d y}{d x} + (3 x + 1) y = e^{- 3 x}

integral of 1/(x^2+2x+65)

\int \frac{1}{x ^{2} + 2 x + 65} d x

derivative of 3sqrt(2x-5)

\frac{d}{d x} (3 2 x - 5)

derivative of 1/(1+4x^2-arctan(2x))

\frac{d}{d x} (\frac{1}{1 + 4 x ^{2}} - arctan (2 x))

Frequently Asked Questions (FAQ)

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