en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

(\partial)/(\partial x)(x^2+4y^2+5z^2)

Solution

\frac{\partial}{\partial x} (x^{2} + 4 y^{2} + 5 z^{2})

Solution

2 x

Solution steps

\frac{\partial}{\partial x} (x^{2} + 4 y^{2} + 5 z^{2})

Treat

y, z

as constants

Apply the Sum/Difference Rule:

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

= \frac{\partial}{\partial x} (x^{2}) + \frac{\partial}{\partial x} (4 y^{2}) + \frac{\partial}{\partial x} (5 z^{2})

\frac{\partial}{\partial x} (x^{2}) = 2 x

\frac{\partial}{\partial x} (4 y^{2}) = 0

\frac{\partial}{\partial x} (5 z^{2}) = 0

= 2 x + 0 + 0

Simplify

= 2 x

Popular Examples

f(x)= 7/10 x^2+4x^3

f (x) = \frac{7}{10} x^{2} + 4 x^{3}

(dp)/(p-p^2)=dt

\frac{d p}{p - p ^{2}} = d t

derivative of 3x^4+2x^3+x^2-2

\frac{d}{d x} (3 x^{4} + 2 x^{3} + x^{2} - 2)

(d^2)/(dx^2)(x^{-2})

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

(dy)/(dx)=-(y(x+y+1))/(x+2y)

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

Frequently Asked Questions (FAQ)

What is (\partial)/(\partial x)(x^2+4y^2+5z^2) ?
The answer to (\partial)/(\partial x)(x^2+4y^2+5z^2) is 2x