What is the derivative of 6x^5ln(x+x^5) ?

The derivative of 6x^5ln(x+x^5) is 30x^4ln(x)+11x^4

What is the first derivative of 6x^5ln(x+x^5) ?

The first derivative of 6x^5ln(x+x^5) is 30x^4ln(x)+11x^4

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\frac{d}{d x} (6 x^{5} ln (x) + x^{5})

30 x^{4} ln (x) + 11 x^{4}

Solution steps

\frac{d}{d x} (6 x^{5} ln (x) + x^{5})

Apply the Sum/Difference Rule:

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

= \frac{d}{d x} (6 x^{5} ln (x)) + \frac{d}{d x} (x^{5})

\frac{d}{d x} (6 x^{5} ln (x)) = 6 (5 x^{4} ln (x) + x^{4})

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

= 6 (5 x^{4} ln (x) + x^{4}) + 5 x^{4}

Simplify

6 (5 x^{4} ln (x) + x^{4}) + 5 x^{4} : 30 x^{4} ln (x) + 11 x^{4}

= 30 x^{4} ln (x) + 11 x^{4}

What is the derivative of 6x^5ln(x+x^5) ?
The derivative of 6x^5ln(x+x^5) is 30x^4ln(x)+11x^4
What is the first derivative of 6x^5ln(x+x^5) ?
The first derivative of 6x^5ln(x+x^5) is 30x^4ln(x)+11x^4