What is the derivative of (8x^2-13x)e^x ?

The derivative of (8x^2-13x)e^x is 8e^xx^2+3e^xx-13e^x

What is the first derivative of (8x^2-13x)e^x ?

The first derivative of (8x^2-13x)e^x is 8e^xx^2+3e^xx-13e^x

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derivative of

(8 x^{2} - 13 x) e^{x}

8 e^{x} x^{2} + 3 e^{x} x - 13 e^{x}

Solution steps

\frac{d}{d x} ((8 x^{2} - 13 x) e^{x})

Apply the Product Rule:

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

f = 8 x^{2} - 13 x, g = e^{x}

= \frac{d}{d x} (8 x^{2} - 13 x) e^{x} + \frac{d}{d x} (e^{x}) (8 x^{2} - 13 x)

\frac{d}{d x} (8 x^{2} - 13 x) = 16 x - 13

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

= (16 x - 13) e^{x} + e^{x} (8 x^{2} - 13 x)

Simplify

(16 x - 13) e^{x} + e^{x} (8 x^{2} - 13 x) : 8 e^{x} x^{2} + 3 e^{x} x - 13 e^{x}

= 8 e^{x} x^{2} + 3 e^{x} x - 13 e^{x}

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

sin (5 t)

y^{^{''}} - y^{^{'}} - 2 y = 8 e - t

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

\frac{\partial}{\partial y} (y + y cos (x y))

What is the derivative of (8x^2-13x)e^x ?
The derivative of (8x^2-13x)e^x is 8e^xx^2+3e^xx-13e^x
What is the first derivative of (8x^2-13x)e^x ?
The first derivative of (8x^2-13x)e^x is 8e^xx^2+3e^xx-13e^x