en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

derivative of xarcsin(x/4+sqrt(16-x^2))

Solution

\frac{d}{d x} (x arcsin (\frac{x}{4}) + 16 - x^{2})

Solution

arcsin (\frac{x}{4})

Solution steps

\frac{d}{d x} (x arcsin (\frac{x}{4}) + 16 - x^{2})

Apply the Sum/Difference Rule:

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

= \frac{d}{d x} (x arcsin (\frac{x}{4})) + \frac{d}{d x} (16 - x^{2})

\frac{d}{d x} (x arcsin (\frac{x}{4})) = arcsin (\frac{x}{4}) + \frac{x}{16 - x ^{2}}

\frac{d}{d x} (16 - x^{2}) = - \frac{x}{16 - x ^{2}}

= arcsin (\frac{x}{4}) + \frac{x}{16 - x ^{2}} - \frac{x}{16 - x ^{2}}

Simplify

= arcsin (\frac{x}{4})

Popular Examples

integral of 45(1+sqrt(x))

\int 45 (1 + x) d x

(\partial)/(\partial x)(ln(x^y))

\frac{\partial}{\partial x} (ln (x^{y}))

limit as x approaches 0 of 1/x-1/(e^t-1)

x \to 0 lim (\frac{1}{x} - \frac{1}{e ^{t} - 1})

limit as x approaches 4 of (3x+4)/(x-2)

x \to 4 lim (\frac{3 x + 4}{x - 2})

derivative of (x-1/(sqrt(x)))

\frac{d}{d x} (\frac{x - 1}{x})

Frequently Asked Questions (FAQ)

What is the derivative of xarcsin(x/4+sqrt(16-x^2)) ?
The derivative of xarcsin(x/4+sqrt(16-x^2)) is arcsin(x/4)
What is the first derivative of xarcsin(x/4+sqrt(16-x^2)) ?
The first derivative of xarcsin(x/4+sqrt(16-x^2)) is arcsin(x/4)