What is the derivative of (3cos(x)(ln(1+x))) ?

The derivative of (3cos(x)(ln(1+x))) is 3(-sin(x)ln(1+x)+(cos(x))/(1+x))

What is the first derivative of (3cos(x)(ln(1+x))) ?

The first derivative of (3cos(x)(ln(1+x))) is 3(-sin(x)ln(1+x)+(cos(x))/(1+x))

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

\frac{d}{d x} ((3 cos (x)) (ln (1 + x)))

3 (- sin (x) ln (1 + x) + \frac{cos ( x )}{1 + x})

Solution steps

\frac{d}{d x} ((3 cos (x)) (ln (1 + x)))

Take the constant out:

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

= 3 \frac{d}{d x} (cos (x) ln (1 + x))

Apply the Product Rule:

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

f = cos (x), g = ln (1 + x)

= 3 (\frac{d}{d x} (cos (x)) ln (1 + x) + \frac{d}{d x} (ln (1 + x)) cos (x))

\frac{d}{d x} (cos (x)) = - sin (x)

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

= 3 ((- sin (x)) ln (1 + x) + \frac{1}{1 + x} cos (x))

Simplify

3 ((- sin (x)) ln (1 + x) + \frac{1}{1 + x} cos (x)) : 3 (- sin (x) ln (1 + x) + \frac{cos ( x )}{1 + x})

= 3 (- sin (x) ln (1 + x) + \frac{cos ( x )}{1 + x})

What is the derivative of (3cos(x)(ln(1+x))) ?
The derivative of (3cos(x)(ln(1+x))) is 3(-sin(x)ln(1+x)+(cos(x))/(1+x))
What is the first derivative of (3cos(x)(ln(1+x))) ?
The first derivative of (3cos(x)(ln(1+x))) is 3(-sin(x)ln(1+x)+(cos(x))/(1+x))