What is the derivative of (4x^2-3xe^{5x}) ?

The derivative of (4x^2-3xe^{5x}) is 20e^{5x}x^2-7e^{5x}x-3e^{5x}

What is the first derivative of (4x^2-3xe^{5x}) ?

The first derivative of (4x^2-3xe^{5x}) is 20e^{5x}x^2-7e^{5x}x-3e^{5x}

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\frac{d}{d x} ((4 x^{2} - 3 x) e^{5 x})

20 e^{5 x} x^{2} - 7 e^{5 x} x - 3 e^{5 x}

Solution steps

\frac{d}{d x} ((4 x^{2} - 3 x) e^{5 x})

Apply the Product Rule:

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

f = 4 x^{2} - 3 x, g = e^{5 x}

= \frac{d}{d x} (4 x^{2} - 3 x) e^{5 x} + \frac{d}{d x} (e^{5 x}) (4 x^{2} - 3 x)

\frac{d}{d x} (4 x^{2} - 3 x) = 8 x - 3

\frac{d}{d x} (e^{5 x}) = e^{5 x} \cdot 5

= (8 x - 3) e^{5 x} + e^{5 x} \cdot 5 (4 x^{2} - 3 x)

Simplify

(8 x - 3) e^{5 x} + e^{5 x} \cdot 5 (4 x^{2} - 3 x) : 20 e^{5 x} x^{2} - 7 e^{5 x} x - 3 e^{5 x}

= 20 e^{5 x} x^{2} - 7 e^{5 x} x - 3 e^{5 x}

\int (cos^{2} (x))^{2} d x

\int \frac{x}{cos ^{2} ( x )} d x

n = 0 \sum \infty \frac{2 n - 1}{n !}

\frac{d}{d x} (- \frac{x}{4})

\int \frac{1}{x ^{2} + x} d x

What is the derivative of (4x^2-3xe^{5x}) ?
The derivative of (4x^2-3xe^{5x}) is 20e^{5x}x^2-7e^{5x}x-3e^{5x}
What is the first derivative of (4x^2-3xe^{5x}) ?
The first derivative of (4x^2-3xe^{5x}) is 20e^{5x}x^2-7e^{5x}x-3e^{5x}