en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

derivative of y=(x^8)/(f(x))

Solution

derivative of

y = \frac{x ^{8}}{f ( x )}

Solution

\frac{8 x ^{7} f ( x ) - \frac{df}{d x} x ^{8}}{f ( x ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{x ^{8}}{f ( x )})

Apply the Quotient Rule:

(\frac{f}{g})^{'} = \frac{f ^{'} \cdot g - g ^{'} \cdot f}{g ^{2}}

= \frac{\frac{d}{d x} ( x ^{8} ) f ( x ) - \frac{df}{d x} x ^{8}}{f ( x ) ^{2}}

\frac{d}{d x} (x^{8}) = 8 x^{7}

= \frac{8 x ^{7} f ( x ) - \frac{df}{d x} x ^{8}}{f ( x ) ^{2}}

Popular Examples

integral of 5cot^5(θ)sin^4(θ)

\int 5 cot^{5} (θ) sin^{4} (θ) d θ

derivative of sqrt(9x)derivative of

9 x

(\partial)/(\partial x)(log_{10}(x+1))

\frac{\partial}{\partial x} (lo g_{10} (x + 1))

limit as x approaches 4 of (5x)/(x-4)

x \to 4 lim (\frac{5 x}{x - 4})

tangent of f(x)=x^2-9x,\at P(x)=3,-15 tangent of

f (x) = x^{2} - 9 x, at P (x) = 3, - 15

Frequently Asked Questions (FAQ)

What is the derivative of y=(x^8)/(f(x)) ?
The derivative of y=(x^8)/(f(x)) is (8x^7f(x)-\frac{df)/(dx)x^8}{f(x)^2}
What is the first derivative of y=(x^8)/(f(x)) ?
The first derivative of y=(x^8)/(f(x)) is (8x^7f(x)-\frac{df)/(dx)x^8}{f(x)^2}