What is the derivative of 100x^{3/4}y^{1/4} ?

The derivative of 100x^{3/4}y^{1/4} is (25(x\frac{dy)/(dx)+3y)}{x^{1/4}y^{3/4}}

What is the first derivative of 100x^{3/4}y^{1/4} ?

The first derivative of 100x^{3/4}y^{1/4} is (25(x\frac{dy)/(dx)+3y)}{x^{1/4}y^{3/4}}

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

\frac{d}{d x} (100 x^{\frac{3}{4}} y^{\frac{1}{4}})

\frac{25 ( x \frac{d y}{d x} + 3 y )}{x ^{\frac{1}{4}} y ^{\frac{3}{4}}}

Solution steps

\frac{d}{d x} (100 x^{\frac{3}{4}} y^{\frac{1}{4}})

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

= 100 \frac{d}{d x} (x^{\frac{3}{4}} y^{\frac{1}{4}})

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = x^{\frac{3}{4}}, g = y^{\frac{1}{4}}

= 100 (\frac{d}{d x} (x^{\frac{3}{4}}) y^{\frac{1}{4}} + \frac{d}{d x} (y^{\frac{1}{4}}) x^{\frac{3}{4}})

\frac{d}{d x} (x^{\frac{3}{4}}) = \frac{3}{4 x ^{\frac{1}{4}}}

\frac{d}{d x} (y^{\frac{1}{4}}) = \frac{\frac{d y}{d x}}{4 y ^{\frac{3}{4}}}

= 100 (\frac{3}{4 x ^{\frac{1}{4}}} y^{\frac{1}{4}} + \frac{\frac{d y}{d x}}{4 y ^{\frac{3}{4}}} x^{\frac{3}{4}})

Simplify

100 (\frac{3}{4 x ^{\frac{1}{4}}} y^{\frac{1}{4}} + \frac{\frac{d y}{d x}}{4 y ^{\frac{3}{4}}} x^{\frac{3}{4}}) : \frac{25 ( x \frac{d y}{d x} + 3 y )}{x ^{\frac{1}{4}} y ^{\frac{3}{4}}}

= \frac{25 ( x \frac{d y}{d x} + 3 y )}{x ^{\frac{1}{4}} y ^{\frac{3}{4}}}

What is the derivative of 100x^{3/4}y^{1/4} ?
The derivative of 100x^{3/4}y^{1/4} is (25(x\frac{dy)/(dx)+3y)}{x^{1/4}y^{3/4}}
What is the first derivative of 100x^{3/4}y^{1/4} ?
The first derivative of 100x^{3/4}y^{1/4} is (25(x\frac{dy)/(dx)+3y)}{x^{1/4}y^{3/4}}