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Popular >

derivative of x^3ln^4(x)

Solution

derivative of

x^{3} ln^{4} (x)

Solution

3 x^{2} ln^{4} (x) + 4 x^{2} ln^{3} (x)

Solution steps

\frac{d}{d x} (x^{3} ln^{4} (x))

Apply the Product Rule:

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

f = x^{3}, g = ln^{4} (x)

= \frac{d}{d x} (x^{3}) ln^{4} (x) + \frac{d}{d x} (ln^{4} (x)) x^{3}

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

\frac{d}{d x} (ln^{4} (x)) = \frac{4 ln ^{3} ( x )}{x}

= 3 x^{2} ln^{4} (x) + \frac{4 ln ^{3} ( x )}{x} x^{3}

\frac{4 ln ^{3} ( x )}{x} x^{3} = 4 x^{2} ln^{3} (x)

= 3 x^{2} ln^{4} (x) + 4 x^{2} ln^{3} (x)

Graph

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Frequently Asked Questions (FAQ)

What is the derivative of x^3ln^4(x) ?
The derivative of x^3ln^4(x) is 3x^2ln^4(x)+4x^2ln^3(x)
What is the first derivative of x^3ln^4(x) ?
The first derivative of x^3ln^4(x) is 3x^2ln^4(x)+4x^2ln^3(x)