What is (\partial)/(\partial x)(3x-(3/4 x+1/4 y)^2) ?

The answer to (\partial)/(\partial x)(3x-(3/4 x+1/4 y)^2) is 3+(-9x-3y)/8

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

(\partial)/(\partial x)(3x-(3/4 x+1/4 y)^2)

\frac{\partial}{\partial x} (3 x - (\frac{3}{4} x + \frac{1}{4} y)^{2})

3 + \frac{- 9 x - 3 y}{8}

Solution steps

\frac{\partial}{\partial x} (3 x - (\frac{3}{4} x + \frac{1}{4} y)^{2})

Simplify

3 x - (\frac{3}{4} x + \frac{1}{4} y)^{2} : 3 x - \frac{( 3 x + y ) ^{2}}{16}

= \frac{\partial}{\partial x} (3 x - \frac{( 3 x + y ) ^{2}}{16})

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

= \frac{\partial}{\partial x} (3 x) - \frac{\partial}{\partial x} (\frac{( 3 x + y ) ^{2}}{16})

\frac{\partial}{\partial x} (3 x) = 3

\frac{\partial}{\partial x} (\frac{( 3 x + y ) ^{2}}{16}) = \frac{3}{8} (3 x + y)

= 3 - \frac{3}{8} (3 x + y)

Simplify

3 - \frac{3}{8} (3 x + y) : 3 + \frac{- 9 x - 3 y}{8}

= 3 + \frac{- 9 x - 3 y}{8}

x \frac{d y}{d x} + (1 + x) y = e^{- x} sin (2 x)

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

\frac{\partial}{\partial x} (4 x e^{x y})

e^{c o s (x)} + cos (e^{x})

x \to 1 lim (1 - x^{2})

What is (\partial)/(\partial x)(3x-(3/4 x+1/4 y)^2) ?
The answer to (\partial)/(\partial x)(3x-(3/4 x+1/4 y)^2) is 3+(-9x-3y)/8