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

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

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

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

Popular >

derivative of

(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}

y^{^{'}} = \frac{y - x y}{x ^{2}}

\int 10 sin^{6} (x) cos^{3} (x) d x

e^{5 x}

x \to o lim (\frac{sin ( 3 x )}{x})

x \to 0 lim (\frac{tan ( 11 x )}{x})

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