What is the derivative of 5Y^{5/8}X^{3/8} ?

The derivative of 5Y^{5/8}X^{3/8} is (25X^{3/8})/(8Y^{3/8)}

What is the first derivative of 5Y^{5/8}X^{3/8} ?

The first derivative of 5Y^{5/8}X^{3/8} is (25X^{3/8})/(8Y^{3/8)}

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derivative of

5 Y^{\frac{5}{8}} X^{\frac{3}{8}}

\frac{25 X ^{\frac{3}{8}}}{8 Y ^{\frac{3}{8}}}

Solution steps

\frac{d}{d Y} (5 Y^{\frac{5}{8}} X^{\frac{3}{8}})

Treat

X

as a constant

Take the constant out:

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

= 5 X^{\frac{3}{8}} \frac{d}{d Y} (Y^{\frac{5}{8}})

Apply the Power Rule:

\frac{d}{d x} (x^{a}) = a \cdot x^{a - 1}

= 5 X^{\frac{3}{8}} \frac{5}{8} Y^{\frac{5}{8} - 1}

Simplify

5 X^{\frac{3}{8}} \frac{5}{8} Y^{\frac{5}{8} - 1} : \frac{25 X ^{\frac{3}{8}}}{8 Y ^{\frac{3}{8}}}

= \frac{25 X ^{\frac{3}{8}}}{8 Y ^{\frac{3}{8}}}

\int \frac{1}{3 x + 12} d x

\frac{\partial}{\partial y} (e^{x + y + 4})

\frac{d y}{d x} = 3 y + 1

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

x sin (x)

What is the derivative of 5Y^{5/8}X^{3/8} ?
The derivative of 5Y^{5/8}X^{3/8} is (25X^{3/8})/(8Y^{3/8)}
What is the first derivative of 5Y^{5/8}X^{3/8} ?
The first derivative of 5Y^{5/8}X^{3/8} is (25X^{3/8})/(8Y^{3/8)}