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Popular >

derivative of xlog_{e}(x)

Solution

\frac{d}{d x} (x lo g_{e} (x))

Solution

ln (x) + 1

Solution steps

\frac{d}{d x} (x lo g_{e} (x))

Simplify

x lo g_{e} (x) : x ln (x)

= \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

Popular Examples

(\partial)/(\partial x)(7xy^9+x^5y^7)

\frac{\partial}{\partial x} (7 x y^{9} + x^{5} y^{7})

derivative of 2x+4/x

\frac{d}{d x} (2 x + \frac{4}{x})

integral of (18)/(1-cos(2x))

\int \frac{18}{1 - cos ( 2 x )} d x

integral of (5x^4)/((10+x^5)^4)

\int \frac{5 x ^{4}}{( 10 + x ^{5} ) ^{4}} d x

integral of (sin(x))/(sec(x))

\int \frac{sin ( x )}{sec ( x )} d x

Frequently Asked Questions (FAQ)

What is the derivative of xlog_{e}(x) ?
The derivative of xlog_{e}(x) is ln(x)+1
What is the first derivative of xlog_{e}(x) ?
The first derivative of xlog_{e}(x) is ln(x)+1