en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

derivative of sin(x+1/(sqrt(x)))

Solution

\frac{d}{d x} (sin (x) + \frac{1}{x})

Solution

cos (x) - \frac{1}{2 x ^{\frac{3}{2}}}

Solution steps

\frac{d}{d x} (sin (x) + \frac{1}{x})

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

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

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

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

= cos (x) - \frac{1}{2 x ^{\frac{3}{2}}}

Graph

Popular Examples

(\partial)/(\partial x)(-3sin(x))

\frac{\partial}{\partial x} (- 3 sin (x))

sum from n=2 to infinity of 1/(n^n)

n = 2 \sum \infty \frac{1}{n ^{n}}

limit as n approaches infinity of n^1

n \to \infty lim (n^{1})

(\partial)/(\partial x)(1/((x^2+y^2+1)))

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

tangent of f(x)=x^2-5x+5,(4,1)tangent of

f (x) = x^{2} - 5 x + 5, (4, 1)

Frequently Asked Questions (FAQ)

What is the derivative of sin(x+1/(sqrt(x))) ?
The derivative of sin(x+1/(sqrt(x))) is cos(x)-1/(2x^{3/2)}
What is the first derivative of sin(x+1/(sqrt(x))) ?
The first derivative of sin(x+1/(sqrt(x))) is cos(x)-1/(2x^{3/2)}