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Popular >

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

Solution

derivative of

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

Solution

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

Solution steps

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

Apply the Product Rule:

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

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

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

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

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

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

Simplify

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

(dy)/(dx)=((-y^2))/((1+y^2))*(e^{-x})

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

derivative of-2sin(x-xcos(x))

\frac{d}{d x} (- 2 sin (x) - x cos (x))

integral of (e^{3sqrt(x)})/(sqrt(x))

\int \frac{e ^{3 x}}{x} d x

tangent of f(x)=(sqrt(x))/(x+1)tangent of

f (x) = \frac{x}{x + 1}

limit as x approaches-2 of 1/((x+2)^5)

x \to - 2 lim (\frac{1}{( x + 2 ) ^{5}})

Frequently Asked Questions (FAQ)

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