What is (\partial)/(\partial y)(y^4+5xy^3) ?

The answer to (\partial)/(\partial y)(y^4+5xy^3) is 4y^3+15xy^2

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

(\partial)/(\partial y)(y^4+5xy^3)

\frac{\partial}{\partial y} (y^{4} + 5 x y^{3})

4 y^{3} + 15 x y^{2}

Solution steps

\frac{\partial}{\partial y} (y^{4} + 5 x y^{3})

Treat

x

as a constant

Apply the Sum/Difference Rule:

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

= \frac{\partial}{\partial y} (y^{4}) + \frac{\partial}{\partial y} (5 x y^{3})

\frac{\partial}{\partial y} (y^{4}) = 4 y^{3}

\frac{\partial}{\partial y} (5 x y^{3}) = 15 x y^{2}

= 4 y^{3} + 15 x y^{2}

\int (54) d x

\int \frac{9 x ^{2}}{1 - x ^{3}} d x

y = x^{2} - 1, y = 0, [0, 3]

f (x) = \frac{1}{4} x - \frac{1}{6}

t y^{^{'}} + 9 y = 3 t

What is (\partial)/(\partial y)(y^4+5xy^3) ?
The answer to (\partial)/(\partial y)(y^4+5xy^3) is 4y^3+15xy^2