What is the derivative of log_{5}(5x^3+2x+5) ?

The derivative of log_{5}(5x^3+2x+5) is (15x^2+2)/(ln(5)(5x^3+2x+5))

What is the first derivative of log_{5}(5x^3+2x+5) ?

The first derivative of log_{5}(5x^3+2x+5) is (15x^2+2)/(ln(5)(5x^3+2x+5))

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

derivative of

lo g_{5} (5 x^{3} + 2 x + 5)

\frac{15 x ^{2} + 2}{ln ( 5 ) ( 5 x ^{3} + 2 x + 5 )}

Solution steps

\frac{d}{d x} (lo g_{5} (5 x^{3} + 2 x + 5))

Apply log rule:

lo g_{a} (b) = \frac{ln ( b )}{ln ( a )}

= \frac{d}{d x} (\frac{ln ( 5 x ^{3} + 2 x + 5 )}{ln ( 5 )})

Take the constant out:

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

= \frac{1}{ln ( 5 )} \frac{d}{d x} (ln (5 x^{3} + 2 x + 5))

Apply the chain rule:

\frac{1}{5 x ^{3} + 2 x + 5} \frac{d}{d x} (5 x^{3} + 2 x + 5)

= \frac{1}{5 x ^{3} + 2 x + 5} \frac{d}{d x} (5 x^{3} + 2 x + 5)

\frac{d}{d x} (5 x^{3} + 2 x + 5) = 15 x^{2} + 2

= \frac{1}{ln ( 5 )} \cdot \frac{1}{5 x ^{3} + 2 x + 5} (15 x^{2} + 2)

Simplify

\frac{1}{ln ( 5 )} \cdot \frac{1}{5 x ^{3} + 2 x + 5} (15 x^{2} + 2) : \frac{15 x ^{2} + 2}{ln ( 5 ) ( 5 x ^{3} + 2 x + 5 )}

= \frac{15 x ^{2} + 2}{ln ( 5 ) ( 5 x ^{3} + 2 x + 5 )}

y^{^{'}} = tan (t) y - 5 t

2916 x, 108 x^{2}

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

\frac{\partial}{\partial x} (sin (5 x) cos (5 y))

\frac{d}{d x} (\frac{x ^{3}}{cos ( x )})

What is the derivative of log_{5}(5x^3+2x+5) ?
The derivative of log_{5}(5x^3+2x+5) is (15x^2+2)/(ln(5)(5x^3+2x+5))
What is the first derivative of log_{5}(5x^3+2x+5) ?
The first derivative of log_{5}(5x^3+2x+5) is (15x^2+2)/(ln(5)(5x^3+2x+5))