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Popular >

derivative of 7x^2ln(x)

Solution

\frac{d}{d x} (7 x^{2} ln (x))

Solution

7 (2 x ln (x) + x)

Solution steps

\frac{d}{d x} (7 x^{2} ln (x))

Take the constant out:

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

= 7 \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)

= 7 (\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}

= 7 (2 x ln (x) + \frac{1}{x} x^{2})

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

= 7 (2 x ln (x) + x)

Popular Examples

derivative of x^3+y^3-3x^2y^2+1 derivative of

x^{3} + y^{3} - 3 x^{2} y^{2} + 1

y^{''}+y^'-2y=2t

y^{^{''}} + y^{^{'}} - 2 y = 2 t

integral from 0 to 3 of x^2

\int_{0}^{3} x^{2} d x

integral of (2x^3+x^2-x)/(x^2)

\int \frac{2 x ^{3} + x ^{2} - x}{x ^{2}} d x

integral of (e^x+x^e)

\int (e^{x} + x^{e}) d x

Frequently Asked Questions (FAQ)

What is the derivative of 7x^2ln(x) ?
The derivative of 7x^2ln(x) is 7(2xln(x)+x)
What is the first derivative of 7x^2ln(x) ?
The first derivative of 7x^2ln(x) is 7(2xln(x)+x)