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Popular >

derivative of 6x^5ln(x+x^5)

Solution

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

Solution

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}

Popular Examples

(dy)/(dx)=8+8y+x+xy

\frac{d y}{d x} = 8 + 8 y + x + x y

d/(dy)(x/(x^2+y^2+1))

\frac{d}{d y} (\frac{x}{x ^{2} + y ^{2} + 1})

limit as x approaches-2 of (5x-4)/(4-x)

x \to - 2 lim (\frac{5 x - 4}{4 - x})

limit as x approaches 0 of (1-cos(4x))/x

x \to 0 lim (\frac{1 - cos ( 4 x )}{x})

integral of 6y-x-4

\int 6 y - x - 4 d y

Frequently Asked Questions (FAQ)

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