What is the derivative of (a+3y^2+b)^{1/2} ?

The derivative of (a+3y^2+b)^{1/2} is (3y)/((a+3y^2+b)^{1/2)}

What is the first derivative of (a+3y^2+b)^{1/2} ?

The first derivative of (a+3y^2+b)^{1/2} is (3y)/((a+3y^2+b)^{1/2)}

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

derivative of

(a + 3 y^{2} + b)^{\frac{1}{2}}

\frac{3 y}{( a + 3 y ^{2} + b ) ^{\frac{1}{2}}}

Solution steps

\frac{d}{d y} ((a + 3 y^{2} + b)^{\frac{1}{2}})

Apply the chain rule:

\frac{1}{2 ( a + 3 y ^{2} + b ) ^{\frac{1}{2}}} \frac{d}{d y} (a + 3 y^{2} + b)

= \frac{1}{2 ( a + 3 y ^{2} + b ) ^{\frac{1}{2}}} \frac{d}{d y} (a + 3 y^{2} + b)

\frac{d}{d y} (a + 3 y^{2} + b) = 6 y

= \frac{1}{2 ( a + 3 y ^{2} + b ) ^{\frac{1}{2}}} \cdot 6 y

Simplify

\frac{1}{2 ( a + 3 y ^{2} + b ) ^{\frac{1}{2}}} \cdot 6 y : \frac{3 y}{( a + 3 y ^{2} + b ) ^{\frac{1}{2}}}

= \frac{3 y}{( a + 3 y ^{2} + b ) ^{\frac{1}{2}}}

f (x) = \frac{π ^{2}}{x ^{2} + 4 x}

\int - \frac{1}{27} sin (3 x) d x

\int \frac{3 - 5 x}{9 - 5 x ^{2}} d x

\frac{d}{d x} (arccos (\frac{6}{x}))

\frac{\partial}{\partial v} (e^{u (v)} + sin (v))

What is the derivative of (a+3y^2+b)^{1/2} ?
The derivative of (a+3y^2+b)^{1/2} is (3y)/((a+3y^2+b)^{1/2)}
What is the first derivative of (a+3y^2+b)^{1/2} ?
The first derivative of (a+3y^2+b)^{1/2} is (3y)/((a+3y^2+b)^{1/2)}