What is the derivative of sin(log_{10}(1+x)) ?

The derivative of sin(log_{10}(1+x)) is (cos(log_{10}(1+x)))/(ln(10)(1+x))

What is the first derivative of sin(log_{10}(1+x)) ?

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

derivative of

sin (lo g_{10} (1 + x))

\frac{cos ( lo g _{10} ( 1 + x ) )}{ln ( 10 ) ( 1 + x )}

Solution steps

\frac{d}{d x} (sin (lo g_{10} (1 + x)))

Apply the chain rule:

cos (lo g_{10} (1 + x)) \frac{d}{d x} (lo g_{10} (1 + x))

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

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

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

Simplify

cos (lo g_{10} (1 + x)) \frac{1}{ln ( 10 ) ( 1 + x )} : \frac{cos ( lo g _{10} ( 1 + x ) )}{ln ( 10 ) ( 1 + x )}

= \frac{cos ( lo g _{10} ( 1 + x ) )}{ln ( 10 ) ( 1 + x )}

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