Expert answers to "Derivatives Find the derivative of the following functions..."

Grady Turner

Answered question

2021-12-07

Derivatives Find the derivative of the following functions for the derivative of

\sqrt{x} \cdot y = x^{5}

William Yazzie

Beginner2021-12-08Added 20 answers

Step 1:Given
The function is

\sqrt{x} \cdot y = x^{5}

Step 2: Simplify and write in terms of y=f(x)

\sqrt{x} \cdot y = x^{5}

Divide both sides by

\sqrt{x}

\frac{\sqrt{x} \cdot y}{\sqrt{x}} = \frac{x^{5}}{\sqrt{x}}

y = \frac{x^{5}}{\sqrt{x}}

y = \frac{x^{5}}{x^{\frac{1}{2}}}

y = x^{5} \cdot x^{- \frac{1}{2}}

y = x^{5} \cdot x^{- \frac{1}{2}}

y = x^{5 - \frac{1}{2}}

y = x^{\frac{9}{2}}

Step 3: Find derivative

y = x^{\frac{9}{2}}

Differentiate with respect to x

\frac{d y}{d x}

= \frac{9}{2} x^{\frac{9}{2} - 1} \dots \frac{d}{d x} x^{n} = n x^{n - 1}

\frac{d y}{d x} = \frac{9}{2} x^{\frac{7}{2}}

Hence,
The derivative of function

\sqrt{x} \cdot y = x^{5} i s \frac{d y}{d x} = \frac{9}{2} x^{72}

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