What is implicit (dy)/(dx),y^4=x^5 ?

The answer to implicit (dy)/(dx),y^4=x^5 is (dy)/(dx)=(5x^4)/(4y^3)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

implicit (dy)/(dx),y^4=x^5

implicit derivative

\frac{d y}{d x}, y^{4} = x^{5}

\frac{d y}{d x} = \frac{5 x ^{4}}{4 y ^{3}}

Solution steps

y^{4} = x^{5}

Treat

y

y (x)

Differentiate both sides:

4 y^{3} \frac{d y}{d x} = 5 x^{4}

Isolate

\frac{d y}{d x} : \frac{d y}{d x} = \frac{5 x ^{4}}{4 y ^{3}}

\frac{d y}{d x} = \frac{5 x ^{4}}{4 y ^{3}}

\int t^{2} e^{4 t} d t

\int 9 x e^{6 x} d x

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

x \to \infty lim (e^{p x} (a cos (q (x) x) + b sin (q (x) x)))

\frac{d y}{d x} = 4 + e^{y - 4 x + 5}

What is implicit (dy)/(dx),y^4=x^5 ?
The answer to implicit (dy)/(dx),y^4=x^5 is (dy)/(dx)=(5x^4)/(4y^3)