What is the derivative of (5x^2-4xe^x) ?

The derivative of (5x^2-4xe^x) is 5e^xx^2+6e^xx-4e^x

What is the first derivative of (5x^2-4xe^x) ?

The first derivative of (5x^2-4xe^x) is 5e^xx^2+6e^xx-4e^x

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\frac{d}{d x} ((5 x^{2} - 4 x) e^{x})

5 e^{x} x^{2} + 6 e^{x} x - 4 e^{x}

Solution steps

\frac{d}{d x} ((5 x^{2} - 4 x) e^{x})

Apply the Product Rule:

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

f = 5 x^{2} - 4 x, g = e^{x}

= \frac{d}{d x} (5 x^{2} - 4 x) e^{x} + \frac{d}{d x} (e^{x}) (5 x^{2} - 4 x)

\frac{d}{d x} (5 x^{2} - 4 x) = 10 x - 4

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

= (10 x - 4) e^{x} + e^{x} (5 x^{2} - 4 x)

Simplify

(10 x - 4) e^{x} + e^{x} (5 x^{2} - 4 x) : 5 e^{x} x^{2} + 6 e^{x} x - 4 e^{x}

= 5 e^{x} x^{2} + 6 e^{x} x - 4 e^{x}

3 x e^{\frac{- 1}{y ^{3}}}

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

y = 11 + cot^{2} (x)

\frac{d}{d x} (I n (x))

\int sin^{4} (θ) cos^{5} (θ) d θ

What is the derivative of (5x^2-4xe^x) ?
The derivative of (5x^2-4xe^x) is 5e^xx^2+6e^xx-4e^x
What is the first derivative of (5x^2-4xe^x) ?
The first derivative of (5x^2-4xe^x) is 5e^xx^2+6e^xx-4e^x