What is the derivative of x^{0.7}y^{0.3} ?

The derivative of x^{0.7}y^{0.3} is (0.7y^{0.3})/(x^{0.3)}+(0.3x^{0.7}\frac{dy)/(dx)}{y^{0.7}}

What is the first derivative of x^{0.7}y^{0.3} ?

The first derivative of x^{0.7}y^{0.3} is (0.7y^{0.3})/(x^{0.3)}+(0.3x^{0.7}\frac{dy)/(dx)}{y^{0.7}}

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\frac{d}{d x} (x^{0.7} y^{0.3})

\frac{0.7 y ^{0.3}}{x ^{0.3}} + \frac{0.3 x ^{0.7} \frac{d y}{d x}}{y ^{0.7}}

Solution steps

\frac{d}{d x} (x^{0.7} y^{0.3})

Apply the Product Rule:

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

f = x^{0.7}, g = y^{0.3}

= \frac{d}{d x} (x^{0.7}) y^{0.3} + \frac{d}{d x} (y^{0.3}) x^{0.7}

\frac{d}{d x} (x^{0.7}) = \frac{0.7}{x ^{0.3}}

\frac{d}{d x} (y^{0.3}) = \frac{0.3 \frac{d y}{d x}}{y ^{0.7}}

= \frac{0.7}{x ^{0.3}} y^{0.3} + \frac{0.3 \frac{d y}{d x}}{y ^{0.7}} x^{0.7}

Simplify

\frac{0.7}{x ^{0.3}} y^{0.3} + \frac{0.3 \frac{d y}{d x}}{y ^{0.7}} x^{0.7} : \frac{0.7 y ^{0.3}}{x ^{0.3}} + \frac{0.3 x ^{0.7} \frac{d y}{d x}}{y ^{0.7}}

= \frac{0.7 y ^{0.3}}{x ^{0.3}} + \frac{0.3 x ^{0.7} \frac{d y}{d x}}{y ^{0.7}}

What is the derivative of x^{0.7}y^{0.3} ?
The derivative of x^{0.7}y^{0.3} is (0.7y^{0.3})/(x^{0.3)}+(0.3x^{0.7}\frac{dy)/(dx)}{y^{0.7}}
What is the first derivative of x^{0.7}y^{0.3} ?
The first derivative of x^{0.7}y^{0.3} is (0.7y^{0.3})/(x^{0.3)}+(0.3x^{0.7}\frac{dy)/(dx)}{y^{0.7}}