What is the derivative of f(x)=xln(x) ?

The derivative of f(x)=xln(x) is ln(x)+1

What is the first derivative of f(x)=xln(x) ?

The first derivative of f(x)=xln(x) is ln(x)+1

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derivative of

f (x) = x ln (x)

ln (x) + 1

Solution steps

\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)

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

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

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

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

Simplify

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

= ln (x) + 1

x^{3}, x^{2} + x, - 1, 1.5

(x^{2} + \frac{1}{4})^{\frac{3}{2}}

\frac{d}{d x} (ln (2 x^{2} + 3))

\int 8 x^{\frac{3}{5}} + 7 x^{- \frac{4}{5}} d x

1 + e^{- t}

What is the derivative of f(x)=xln(x) ?
The derivative of f(x)=xln(x) is ln(x)+1
What is the first derivative of f(x)=xln(x) ?
The first derivative of f(x)=xln(x) is ln(x)+1