What is the derivative of (y^4)/(x^{12)}+8e^x ?

The derivative of (y^4)/(x^{12)}+8e^x is (4y^3)/(x^{12)}

What is the first derivative of (y^4)/(x^{12)}+8e^x ?

The first derivative of (y^4)/(x^{12)}+8e^x is (4y^3)/(x^{12)}

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

derivative of

\frac{y ^{4}}{x ^{12}} + 8 e^{x}

\frac{4 y ^{3}}{x ^{12}}

Solution steps

\frac{d}{d y} (\frac{y ^{4}}{x ^{12}} + 8 e^{x})

Treat

x

as a constant

Apply the Sum/Difference Rule:

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

= \frac{d}{d y} (\frac{y ^{4}}{x ^{12}}) + \frac{d}{d y} (8 e^{x})

\frac{d}{d y} (\frac{y ^{4}}{x ^{12}}) = \frac{4 y ^{3}}{x ^{12}}

\frac{d}{d y} (8 e^{x}) = 0

= \frac{4 y ^{3}}{x ^{12}} + 0

Simplify

= \frac{4 y ^{3}}{x ^{12}}

\int_{0}^{5} (x e^{- x}) d x

\frac{d}{d x} (2 + x x)

y = (x^{5} + 1)^{7}

\frac{d y}{d x} - y = 2 e^{x} y^{2}

\int t \cdot sin (t) d t

What is the derivative of (y^4)/(x^{12)}+8e^x ?
The derivative of (y^4)/(x^{12)}+8e^x is (4y^3)/(x^{12)}
What is the first derivative of (y^4)/(x^{12)}+8e^x ?
The first derivative of (y^4)/(x^{12)}+8e^x is (4y^3)/(x^{12)}