Fractions and Decimals

Discrete Mathematics

Differential Equations

Solved on Sep 30, 2023

Find the derivative $\frac{d y}{d x}$ when $x=\sqrt{y}$ .

STEP 1

Question: Which of the following is an equivalent form of the equation $x=\sqrt{y}$ ?
A) $y=x^3$ B) $y=x^2$ C) $y=2x$ D) $y=x$
Answer: B) $y=x^2$

STEP 2

Question: What does $\frac{d y}{d x}$ represent in calculus?
A) The integral of y with respect to x B) The derivative of y with respect to x C) The limit of y as x approaches infinity D) The area under the curve y=x
Answer: B) The derivative of y with respect to x

STEP 3

Question: What is the power rule in calculus?
A) The derivative of $x^n$ is $n \cdot x^{n-1}$ B) The derivative of $x^n$ is $n \cdot x^{n+1}$ C) The derivative of $x^n$ is $n \cdot x^{n}$ D) The derivative of $x^n$ is $n \cdot x^{n/2}$
Answer: A) The derivative of $x^n$ is $n \cdot x^{n-1}$

STEP 4

Question: What is the derivative of $x^2$ according to the power rule?
A) $2x^2$ B) $2x$ C) $x^2$ D) $4x$
Answer: B) $2x$

STEP 5

Question: What is the derivative of $y$ with respect to $x$ in the equation $y=x^2$ ?
A) $2x^2$ B) $2x$ C) $x^2$ D) $4x$
Answer: B) $2x$

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