What is the derivative of f(x)=5sqrt(x)ln(x) ?

The derivative of f(x)=5sqrt(x)ln(x) is 5((ln(x))/(2sqrt(x))+1/(sqrt(x)))

What is the first derivative of f(x)=5sqrt(x)ln(x) ?

The first derivative of f(x)=5sqrt(x)ln(x) is 5((ln(x))/(2sqrt(x))+1/(sqrt(x)))

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derivative of

f (x) = 5 x ln (x)

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

Solution steps

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

Take the constant out:

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

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

Apply the Product Rule:

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

f = x, g = ln (x)

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

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

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

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

Simplify

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

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

What is the derivative of f(x)=5sqrt(x)ln(x) ?
The derivative of f(x)=5sqrt(x)ln(x) is 5((ln(x))/(2sqrt(x))+1/(sqrt(x)))
What is the first derivative of f(x)=5sqrt(x)ln(x) ?
The first derivative of f(x)=5sqrt(x)ln(x) is 5((ln(x))/(2sqrt(x))+1/(sqrt(x)))