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Popular >

derivative of 5x^5ln(x)

Solution

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

Solution

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

Solution steps

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

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

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

Apply the Product Rule:

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

f = x^{5}, g = ln (x)

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

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

\frac{d}{d x} (ln (x)) = \frac{1}{x}

= 5 (5 x^{4} ln (x) + \frac{1}{x} x^{5})

\frac{1}{x} x^{5} = x^{4}

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

Popular Examples

integral from 3 to 4 of (2x-3)/6

\int_{3}^{4} \frac{2 x - 3}{6} d x

integral from 2 to 3 of (3-x)

\int_{2}^{3} (3 - x) d x

integral of p^5ln(p)

\int p^{5} ln (p) d p

(dy)/(dx)=(xy+2)/(x+1)

\frac{d y}{d x} = \frac{x y + 2}{x + 1}

d/(dt)(t-cos(t))

\frac{d}{d t} (t - cos (t))

Frequently Asked Questions (FAQ)

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