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Popular >

derivative of (x^2+3x-1)e^x

Solution

derivative of

(x^{2} + 3 x - 1) e^{x}

Solution

e^{x} x^{2} + 5 e^{x} x + 2 e^{x}

Solution steps

\frac{d}{d x} ((x^{2} + 3 x - 1) e^{x})

Apply the Product Rule:

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

f = x^{2} + 3 x - 1, g = e^{x}

= \frac{d}{d x} (x^{2} + 3 x - 1) e^{x} + \frac{d}{d x} (e^{x}) (x^{2} + 3 x - 1)

\frac{d}{d x} (x^{2} + 3 x - 1) = 2 x + 3

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

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

Simplify

(2 x + 3) e^{x} + e^{x} (x^{2} + 3 x - 1) : e^{x} x^{2} + 5 e^{x} x + 2 e^{x}

= e^{x} x^{2} + 5 e^{x} x + 2 e^{x}

Popular Examples

(\partial)/(\partial y)(ycos(x)+2xe^y-x)

\frac{\partial}{\partial y} (y cos (x) + 2 x e^{y} - x)

tangent of f(x)=3x^2-4x+6,\at x=2 tangent of

f (x) = 3 x^{2} - 4 x + 6, at x = 2

tangent of f(x)=x^3-3x+4,(3,22)tangent of

f (x) = x^{3} - 3 x + 4, (3, 22)

derivative of 1+x^4

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

tangent of f(x)=(x^2)/(x-8)tangent of

f (x) = \frac{x ^{2}}{x - 8}

Frequently Asked Questions (FAQ)

What is the derivative of (x^2+3x-1)e^x ?
The derivative of (x^2+3x-1)e^x is e^xx^2+5e^xx+2e^x
What is the first derivative of (x^2+3x-1)e^x ?
The first derivative of (x^2+3x-1)e^x is e^xx^2+5e^xx+2e^x