What is the derivative of x^2log_{10}(1/x) ?

The derivative of x^2log_{10}(1/x) is -(x+2xln(x))/(ln(10))

What is the first derivative of x^2log_{10}(1/x) ?

The first derivative of x^2log_{10}(1/x) is -(x+2xln(x))/(ln(10))

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derivative of

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

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

Solution steps

\frac{d}{d x} (x^{2} lo g_{10} (\frac{1}{x}))

Simplify

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

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

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

= - \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 )}

\frac{1}{( 1 - x ^{2} )}

sin (x) + ln (x^{2}) + e^{2} x

6 x^{\frac{1}{3}}

(\frac{x ^{5} + 1}{x}) (x^{5} + 1)

4 x - 5

What is the derivative of x^2log_{10}(1/x) ?
The derivative of x^2log_{10}(1/x) is -(x+2xln(x))/(ln(10))
What is the first derivative of x^2log_{10}(1/x) ?
The first derivative of x^2log_{10}(1/x) is -(x+2xln(x))/(ln(10))