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))

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

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 )}

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))