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Popular >

(xln(x))^'

Solution

(x ln (x))^{^{'}}

Solution

ln (x) + 1

Solution steps

(x ln (x))^{'}

Apply the Product Rule:

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

f = x, g = ln (x)

= x^{^{'}} ln (x) + (ln (x))^{^{'}} x

x^{'} = 1

(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

Graph

Popular Examples

(d^2y)/(dx^2)+derivative of 2y+y=0

\frac{d ^{2} y}{d x ^{2}} + \frac{d}{d x} (2 y) + y = 0

(\partial)/(\partial x)(1+6x^2+3y)

\frac{\partial}{\partial x} (1 + 6 x^{2} + 3 y)

integral of (x^3-2sqrt(x))/x

\int \frac{x ^{3} - 2 x}{x} d x

integral of (6x+1)*sqrt(2x-3)

\int (6 x + 1) \cdot 2 x - 3 d x

tangent of f(x)=(1+2x)(3-2x),\at x=1 tangent of

f (x) = (1 + 2 x) (3 - 2 x), at x = 1

Frequently Asked Questions (FAQ)

What is the (xln(x))^' ?
The (xln(x))^' is ln(x)+1
What is the first (xln(x))^' ?
The first (xln(x))^' is ln(x)+1