What is the derivative of f(x)=sin(x)ln(x^4+1/x) ?

The derivative of f(x)=sin(x)ln(x^4+1/x) is cos(x)ln(x^4+1/x)+(sin(x)(4x^5-1))/(x(x^5+1))

What is the first derivative of f(x)=sin(x)ln(x^4+1/x) ?

The first derivative of f(x)=sin(x)ln(x^4+1/x) is cos(x)ln(x^4+1/x)+(sin(x)(4x^5-1))/(x(x^5+1))

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

derivative of

f (x) = sin (x) ln (x^{4} + \frac{1}{x})

cos (x) ln (x^{4} + \frac{1}{x}) + \frac{sin ( x ) ( 4 x ^{5} - 1 )}{x ( x ^{5} + 1 )}

Solution steps

\frac{d}{d x} (sin (x) ln (x^{4} + \frac{1}{x}))

Apply the Product Rule:

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

f = sin (x), g = ln (x^{4} + \frac{1}{x})

= \frac{d}{d x} (sin (x)) ln (x^{4} + \frac{1}{x}) + \frac{d}{d x} (ln (x^{4} + \frac{1}{x})) sin (x)

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

\frac{d}{d x} (ln (x^{4} + \frac{1}{x})) = \frac{4 x ^{5} - 1}{x ( x ^{5} + 1 )}

= cos (x) ln (x^{4} + \frac{1}{x}) + \frac{4 x ^{5} - 1}{x ( x ^{5} + 1 )} sin (x)

Multiply fractions:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= cos (x) ln (x^{4} + \frac{1}{x}) + \frac{sin ( x ) ( 4 x ^{5} - 1 )}{x ( x ^{5} + 1 )}

\frac{d}{d x} (\frac{1}{x ^{3} - 4 x})

\int \frac{27}{27 + e ^{x}} d x

x^{\frac{11}{2}}

\frac{\partial}{\partial x} (arctan (x^{2} + 1))

\int \frac{5}{x - 1} d x

What is the derivative of f(x)=sin(x)ln(x^4+1/x) ?
The derivative of f(x)=sin(x)ln(x^4+1/x) is cos(x)ln(x^4+1/x)+(sin(x)(4x^5-1))/(x(x^5+1))
What is the first derivative of f(x)=sin(x)ln(x^4+1/x) ?
The first derivative of f(x)=sin(x)ln(x^4+1/x) is cos(x)ln(x^4+1/x)+(sin(x)(4x^5-1))/(x(x^5+1))