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

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

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

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

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derivative of

f (x) = x \cdot 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

\frac{\partial}{\partial x} (x^{8} + 6 x y^{7})

6 + \frac{1}{x ^{2}}

y^{^{''}} + 4 y = 3 cos (2 t) - 5 sin (2 t)

y = x^{4} - 4 x^{2} + 10, at x = 1

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

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