What is the derivative of f(x)=(6x^2-10x)e^x ?

The derivative of f(x)=(6x^2-10x)e^x is 6e^xx^2+2e^xx-10e^x

What is the first derivative of f(x)=(6x^2-10x)e^x ?

The first derivative of f(x)=(6x^2-10x)e^x is 6e^xx^2+2e^xx-10e^x

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derivative of

f (x) = (6 x^{2} - 10 x) e^{x}

6 e^{x} x^{2} + 2 e^{x} x - 10 e^{x}

Solution steps

\frac{d}{d x} ((6 x^{2} - 10 x) e^{x})

Apply the Product Rule:

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

f = 6 x^{2} - 10 x, g = e^{x}

= \frac{d}{d x} (6 x^{2} - 10 x) e^{x} + \frac{d}{d x} (e^{x}) (6 x^{2} - 10 x)

\frac{d}{d x} (6 x^{2} - 10 x) = 12 x - 10

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

= (12 x - 10) e^{x} + e^{x} (6 x^{2} - 10 x)

Simplify

(12 x - 10) e^{x} + e^{x} (6 x^{2} - 10 x) : 6 e^{x} x^{2} + 2 e^{x} x - 10 e^{x}

= 6 e^{x} x^{2} + 2 e^{x} x - 10 e^{x}

\int (sec^{2} (θ) + 5) d θ

\frac{d y}{d x} + y^{9} x + 7 y = 0

\int \frac{2 x ^{2} + 3}{x ^{3}} d x

\frac{\partial}{\partial x} (2 x^{2} y - x^{3})

n = 1 \sum \infty \frac{2}{3 ^{n + 1}}

What is the derivative of f(x)=(6x^2-10x)e^x ?
The derivative of f(x)=(6x^2-10x)e^x is 6e^xx^2+2e^xx-10e^x
What is the first derivative of f(x)=(6x^2-10x)e^x ?
The first derivative of f(x)=(6x^2-10x)e^x is 6e^xx^2+2e^xx-10e^x