What is the derivative of xlog_{10}(x) ?

The derivative of xlog_{10}(x) is log_{10}(x)+1/(ln(10))

What is the first derivative of xlog_{10}(x) ?

The first derivative of xlog_{10}(x) is log_{10}(x)+1/(ln(10))

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\frac{d}{d x} (x lo g_{10} (x))

lo g_{10} (x) + \frac{1}{ln ( 10 )}

Solution steps

\frac{d}{d x} (x lo g_{10} (x))

Apply the Product Rule:

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

f = x, g = lo g_{10} (x)

= \frac{d x}{d x} lo g_{10} (x) + \frac{d}{d x} (lo g_{10} (x)) x

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

\frac{d}{d x} (lo g_{10} (x)) = \frac{1}{x ln ( 10 )}

= 1 \cdot lo g_{10} (x) + \frac{1}{x ln ( 10 )} x

Simplify

1 \cdot lo g_{10} (x) + \frac{1}{x ln ( 10 )} x : lo g_{10} (x) + \frac{1}{ln ( 10 )}

= lo g_{10} (x) + \frac{1}{ln ( 10 )}

\int y sin (x y) d x

\frac{d}{d x} (- 4 x^{10})

\frac{d y}{d t} = - 3 y + 12

\int (x - 4) sin (π x) d x

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

What is the derivative of xlog_{10}(x) ?
The derivative of xlog_{10}(x) is log_{10}(x)+1/(ln(10))
What is the first derivative of xlog_{10}(x) ?
The first derivative of xlog_{10}(x) is log_{10}(x)+1/(ln(10))