What is (\partial)/(\partial y)(xsqrt(1+y^9)) ?

The answer to (\partial)/(\partial y)(xsqrt(1+y^9)) is (9xy^8)/(2sqrt(1+y^9))

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

(\partial)/(\partial y)(xsqrt(1+y^9))

\frac{\partial}{\partial y} (x 1 + y^{9})

\frac{9 x y ^{8}}{2 1 + y ^{9}}

Solution steps

\frac{\partial}{\partial y} (x 1 + y^{9})

Treat

x

as a constant

Take the constant out:

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

= x \frac{\partial}{\partial y} (1 + y^{9})

Apply the chain rule:

\frac{1}{2 1 + y ^{9}} \frac{\partial}{\partial y} (1 + y^{9})

= \frac{1}{2 1 + y ^{9}} \frac{\partial}{\partial y} (1 + y^{9})

\frac{\partial}{\partial y} (1 + y^{9}) = 9 y^{8}

= x \frac{1}{2 1 + y ^{9}} \cdot 9 y^{8}

Simplify

x \frac{1}{2 1 + y ^{9}} \cdot 9 y^{8} : \frac{9 x y ^{8}}{2 1 + y ^{9}}

= \frac{9 x y ^{8}}{2 1 + y ^{9}}

\frac{6 x}{3 - tan ( x )}

\int 8 sin^{4} (r) cos (r) d r

\int x^{2} sin (4 x^{3} + 7) d x

f (x) = 18 x - 3 x^{2}

\int \frac{1}{z ^{2} 9 - z ^{2}} d z

What is (\partial)/(\partial y)(xsqrt(1+y^9)) ?
The answer to (\partial)/(\partial y)(xsqrt(1+y^9)) is (9xy^8)/(2sqrt(1+y^9))