What is implicit (dy)/(dx),y^5=x^8 ?

The answer to implicit (dy)/(dx),y^5=x^8 is (dy)/(dx)=(8x^7)/(5y^4)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

implicit (dy)/(dx),y^5=x^8

implicit derivative

\frac{d y}{d x}, y^{5} = x^{8}

\frac{d y}{d x} = \frac{8 x ^{7}}{5 y ^{4}}

Solution steps

y^{5} = x^{8}

Treat

y

y (x)

Differentiate both sides:

5 y^{4} \frac{d y}{d x} = 8 x^{7}

Isolate

\frac{d y}{d x} : \frac{d y}{d x} = \frac{8 x ^{7}}{5 y ^{4}}

\frac{d y}{d x} = \frac{8 x ^{7}}{5 y ^{4}}

\int x (5^{- x^{2}}) d x

\int 1 - x d x

\int (3 x^{4} - 4 x^{3} + 6 x^{2} - \frac{x}{2} + 3) d x

\int 8 tan (x) sin (y) cos (y) d x

\frac{d}{d x} ((2 x^{2} - 7)^{5} - (1 + 4 x^{3})^{5})

What is implicit (dy)/(dx),y^5=x^8 ?
The answer to implicit (dy)/(dx),y^5=x^8 is (dy)/(dx)=(8x^7)/(5y^4)