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Popular >

derivative of 5xln(3x)

Solution

\frac{d}{d x} (5 x ln (3 x))

Solution

5 (ln (3 x) + 1)

Solution steps

\frac{d}{d x} (5 x ln (3 x))

Take the constant out:

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

= 5 \frac{d}{d x} (x ln (3 x))

Apply the Product Rule:

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

f = x, g = ln (3 x)

= 5 (\frac{d x}{d x} ln (3 x) + \frac{d}{d x} (ln (3 x)) x)

\frac{d x}{d x} = 1

\frac{d}{d x} (ln (3 x)) = \frac{1}{x}

= 5 (1 \cdot ln (3 x) + \frac{1}{x} x)

Simplify

5 (1 \cdot ln (3 x) + \frac{1}{x} x) : 5 (ln (3 x) + 1)

= 5 (ln (3 x) + 1)

Popular Examples

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\frac{\partial}{\partial x} (x cos (y))

integral of x^2cos(x^3+10)

\int x^{2} cos (x^{3} + 10) d x

taylor ln(1-x)taylor

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\int \frac{y ^{5}}{1 - y ^{4}} d y

(\partial)/(\partial t)(s/t)

\frac{\partial}{\partial t} (\frac{s}{t})

Frequently Asked Questions (FAQ)

What is the derivative of 5xln(3x) ?
The derivative of 5xln(3x) is 5(ln(3x)+1)
What is the first derivative of 5xln(3x) ?
The first derivative of 5xln(3x) is 5(ln(3x)+1)