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Popular Calculus >

derivative of 3e^x+8x^2ln^2(x)

Solution

\frac{d}{d x} (3 e^{x} + 8 x^{2} ln^{2} (x))

Solution

3 e^{x} + 8 (2 x ln^{2} (x) + 2 x ln (x))

Solution steps

\frac{d}{d x} (3 e^{x} + 8 x^{2} ln^{2} (x))

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{d}{d x} (3 e^{x}) + \frac{d}{d x} (8 x^{2} ln^{2} (x))

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

\frac{d}{d x} (8 x^{2} ln^{2} (x)) = 8 (2 x ln^{2} (x) + 2 x ln (x))

= 3 e^{x} + 8 (2 x ln^{2} (x) + 2 x ln (x))

Graph

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Frequently Asked Questions (FAQ)

What is the derivative of 3e^x+8x^2ln^2(x) ?
The derivative of 3e^x+8x^2ln^2(x) is 3e^x+8(2xln^2(x)+2xln(x))
What is the first derivative of 3e^x+8x^2ln^2(x) ?
The first derivative of 3e^x+8x^2ln^2(x) is 3e^x+8(2xln^2(x)+2xln(x))