What is the derivative of x\times log_{10}(x) ?

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

What is the first derivative of x\times log_{10}(x) ?

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

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\frac{d}{d x} (x \cdot 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 tan^{3} (x) sec^{10} (x) d x

\int 6 x (x^{2} + 1)^{\frac{1}{2}} d x

\int (3 x - sin (x)) d x

\frac{\partial}{\partial y} (2 x^{3} y - 3)

\frac{5 X ^{4} - 3 X ^{3}}{X ^{5}}

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