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Popular Calculus >

derivative of 5x^4ln(x+x^4)

Solution

\frac{d}{d x} (5 x^{4} ln (x) + x^{4})

Solution

20 x^{3} ln (x) + 9 x^{3}

Solution steps

\frac{d}{d x} (5 x^{4} ln (x) + x^{4})

Apply the Sum/Difference Rule:

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

= \frac{d}{d x} (5 x^{4} ln (x)) + \frac{d}{d x} (x^{4})

\frac{d}{d x} (5 x^{4} ln (x)) = 5 (4 x^{3} ln (x) + x^{3})

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

= 5 (4 x^{3} ln (x) + x^{3}) + 4 x^{3}

Simplify

5 (4 x^{3} ln (x) + x^{3}) + 4 x^{3} : 20 x^{3} ln (x) + 9 x^{3}

= 20 x^{3} ln (x) + 9 x^{3}

Graph

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Frequently Asked Questions (FAQ)

What is the derivative of 5x^4ln(x+x^4) ?
The derivative of 5x^4ln(x+x^4) is 20x^3ln(x)+9x^3
What is the first derivative of 5x^4ln(x+x^4) ?
The first derivative of 5x^4ln(x+x^4) is 20x^3ln(x)+9x^3