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Popular >

derivative of 5x^2ln(x)

Solution

\frac{d}{d x} (5 x^{2} ln (x))

Solution

5 (2 x ln (x) + x)

Solution steps

\frac{d}{d x} (5 x^{2} ln (x))

Take the constant out:

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

= 5 \frac{d}{d x} (x^{2} ln (x))

Apply the Product Rule:

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

f = x^{2}, g = ln (x)

= 5 (\frac{d}{d x} (x^{2}) ln (x) + \frac{d}{d x} (ln (x)) x^{2})

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

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

= 5 (2 x ln (x) + \frac{1}{x} x^{2})

\frac{1}{x} x^{2} = x

= 5 (2 x ln (x) + x)

Popular Examples

tangent of (x^3-16x)^{14}tangent of

(x^{3} - 16 x)^{14}

integral of 36x^2

\int 36 x^{2} d x

integral of (9x)/((7-x^2)^3)

\int \frac{9 x}{( 7 - x ^{2} ) ^{3}} d x

limit as x approaches 0 of 1+e^{1/x}

x \to 0 lim (1 + e^{\frac{1}{x}})

integral of (x^2)/(x^4-42x^2-343)

\int \frac{x ^{2}}{x ^{4} - 42 x ^{2} - 343} d x

Frequently Asked Questions (FAQ)

What is the derivative of 5x^2ln(x) ?
The derivative of 5x^2ln(x) is 5(2xln(x)+x)
What is the first derivative of 5x^2ln(x) ?
The first derivative of 5x^2ln(x) is 5(2xln(x)+x)