What is the derivative of x^2log_{10}(x) ?

The derivative of x^2log_{10}(x) is (x+2xln(x))/(ln(10))

What is the first derivative of x^2log_{10}(x) ?

The first derivative of x^2log_{10}(x) is (x+2xln(x))/(ln(10))

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\frac{d}{d x} (x^{2} lo g_{10} (x))

\frac{x + 2 x ln ( x )}{ln ( 10 )}

Solution steps

\frac{d}{d x} (x^{2} lo g_{10} (x))

Apply the Product Rule:

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

f = x^{2}, g = lo g_{10} (x)

= \frac{d}{d x} (x^{2}) lo g_{10} (x) + \frac{d}{d x} (lo g_{10} (x)) x^{2}

\frac{d}{d x} (x^{2}) = 2 x

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

= 2 x lo g_{10} (x) + \frac{1}{x ln ( 10 )} x^{2}

Simplify

2 x lo g_{10} (x) + \frac{1}{x ln ( 10 )} x^{2} : \frac{x + 2 x ln ( x )}{ln ( 10 )}

= \frac{x + 2 x ln ( x )}{ln ( 10 )}

What is the derivative of x^2log_{10}(x) ?
The derivative of x^2log_{10}(x) is (x+2xln(x))/(ln(10))
What is the first derivative of x^2log_{10}(x) ?
The first derivative of x^2log_{10}(x) is (x+2xln(x))/(ln(10))