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Popular >

derivative of f(x)=(3x^2-5x)e^x

Solution

derivative of

f (x) = (3 x^{2} - 5 x) e^{x}

Solution

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

Solution steps

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

Apply the Product Rule:

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

f = 3 x^{2} - 5 x, g = e^{x}

= \frac{d}{d x} (3 x^{2} - 5 x) e^{x} + \frac{d}{d x} (e^{x}) (3 x^{2} - 5 x)

\frac{d}{d x} (3 x^{2} - 5 x) = 6 x - 5

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

= (6 x - 5) e^{x} + e^{x} (3 x^{2} - 5 x)

Simplify

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

= 3 e^{x} x^{2} + e^{x} x - 5 e^{x}

Popular Examples

derivative of f(t)=(t^{62}+3t+3)(5t^2+4)derivative of

f (t) = (t^{62} + 3 t + 3) (5 t^{2} + 4)

derivative of sqrt(ln(7x))

\frac{d}{d x} (ln (7 x))

(\partial)/(\partial x)((xy-1)^2)

\frac{\partial}{\partial x} ((x y - 1)^{2})

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

\int \frac{x ^{4} + 4}{x ^{3}} d x

y^{''}+3y^'+2y=e^{-2t}

y^{^{''}} + 3 y^{^{'}} + 2 y = e^{- 2 t}

Frequently Asked Questions (FAQ)

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