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

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

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

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

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derivative of

y = x ln (x)

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

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}{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}

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

Simplify

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

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

θ \to - \frac{π}{2} - lim (sec (θ))

\frac{d}{d x} (\frac{x}{36 + x ^{2}})

\frac{\partial}{\partial x} (2 x e^{x^{2}} + y^{2})

y^{^{''}} + 6 y^{^{'}} + 18 y = 0

y \to 0 lim (cot (5 y))

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