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Popular >

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

Solution

derivative of

f (x) = (x^{2} + 1) \cdot 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

81y^{''}+72y^'+16y=0,y^'(0)=-1

81 y^{^{''}} + 72 y^{^{'}} + 16 y = 0, y^{^{'}} (0) = - 1

derivative of x^{9/4}+e^{-2x}

\frac{d}{d x} (x^{\frac{9}{4}} + e^{- 2 x})

2(dy)/(dx)+6y+4=0

2 \frac{d y}{d x} + 6 y + 4 = 0

derivative of f(x)=(3x^2+3x-1)^4 derivative of

f (x) = (3 x^{2} + 3 x - 1)^{4}

integral of x*sin(x)*cos(x)

\int x \cdot sin (x) \cdot cos (x) d x

Frequently Asked Questions (FAQ)

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