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Popular >

derivative of 5x^2e^{3x-7}

Solution

\frac{d}{d x} (5 x^{2} e^{3 x - 7})

Solution

5 (2 x e^{3 x - 7} + e^{3 x - 7} \cdot 3 x^{2})

Solution steps

\frac{d}{d x} (5 x^{2} e^{3 x - 7})

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

= 5 \frac{d}{d x} (x^{2} e^{3 x - 7})

Apply the Product Rule:

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

f = x^{2}, g = e^{3 x - 7}

= 5 (\frac{d}{d x} (x^{2}) e^{3 x - 7} + \frac{d}{d x} (e^{3 x - 7}) x^{2})

\frac{d}{d x} (x^{2}) = 2 x

\frac{d}{d x} (e^{3 x - 7}) = e^{3 x - 7} \cdot 3

= 5 (2 x e^{3 x - 7} + e^{3 x - 7} \cdot 3 x^{2})

Popular Examples

derivative of f(x)= 6/(ln(x))derivative of

f (x) = \frac{6}{ln ( x )}

derivative of 1/(\sqrt[3]{3-x^3})

(dy)/(dx)+3/x y=16y^3

\frac{d y}{d x} + \frac{3}{x} y = 16 y^{3}

integral from 4 to 7 of x/(x^2+6x+13)

\int_{4}^{7} \frac{x}{x ^{2} + 6 x + 13} d x

tangent of f(x)=2x^2+2x,\at x=-3 tangent of

f (x) = 2 x^{2} + 2 x, at x = - 3

Frequently Asked Questions (FAQ)

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