What is the derivative of sqrt(x)ln(10x) ?

The derivative of sqrt(x)ln(10x) is (ln(10x))/(2sqrt(x))+1/(sqrt(x))

What is the first derivative of sqrt(x)ln(10x) ?

The first derivative of sqrt(x)ln(10x) is (ln(10x))/(2sqrt(x))+1/(sqrt(x))

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\frac{d}{d x} (x ln (10 x))

\frac{ln ( 10 x )}{2 x} + \frac{1}{x}

Solution steps

\frac{d}{d x} (x ln (10 x))

Apply the Product Rule:

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

f = x, g = ln (10 x)

= \frac{d}{d x} (x) ln (10 x) + \frac{d}{d x} (ln (10 x)) x

\frac{d}{d x} (x) = \frac{1}{2 x}

\frac{d}{d x} (ln (10 x)) = \frac{1}{x}

= \frac{1}{2 x} ln (10 x) + \frac{1}{x} x

Simplify

\frac{1}{2 x} ln (10 x) + \frac{1}{x} x : \frac{ln ( 10 x )}{2 x} + \frac{1}{x}

= \frac{ln ( 10 x )}{2 x} + \frac{1}{x}

\int \frac{( 2 x - 1 ) e ^{x^{2}}}{e ^{x}} d x

f (t) = 1 \cdot t^{3}

\frac{d}{d x} (x + lo g_{e} (x))

x^{2} - x

\frac{d x}{d t} - 4 x = cos (5 t)

What is the derivative of sqrt(x)ln(10x) ?
The derivative of sqrt(x)ln(10x) is (ln(10x))/(2sqrt(x))+1/(sqrt(x))
What is the first derivative of sqrt(x)ln(10x) ?
The first derivative of sqrt(x)ln(10x) is (ln(10x))/(2sqrt(x))+1/(sqrt(x))