y=sqrt(4x+1) (dy)/(dx)=? Choose 1 answer: (A) (2)/(sqrt(4x+1)) (B) 2sqrt(4x+1) (C) (2)/(sqrtx) (D) (1)/(2sqrt(4x+1))

Apply Chain Rule: To find the derivative of y with respect to x, we will use the chain rule. The chain rule states that the derivative of a composite function is the derivative of the outer function evaluated at the inner function times the derivative of the inner function.Identify Outer and Inner Functions: The outer function is the square root function, and the inner function is (4x+1). The derivative of the outer function, sqrt(u), with respect to u is (1/2)sqrt(u). The derivative of the inner function, 4x+1, with respect to x is 4.Calculate Derivative: Applying the chain rule, we multiply the derivative of the outer function by the derivative of the inner function. This gives us (1/2)sqrt(4x+1) * 4.Simplify Expression: Simplify the expression by multiplying (1/2) by 4, which gives us 2. So the derivative is 2/sqrt(4x+1).

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y=sqrt(4x+1)

(dy)/(dx)=?
Choose 1 answer:
(A)
(2)/(sqrt(4x+1))
(B)
2sqrt(4x+1)
(C)
(2)/(sqrtx)
(D)
(1)/(2sqrt(4x+1))

$y=\sqrt{4 x+1}$ $\newline$ $\frac{d y}{d x}=?$ $\newline$ Choose $1$ answer: $\newline$ (A) $\frac{2}{\sqrt{4 x+1}}$ $\newline$ (B) $2 \sqrt{4 x+1}$ $\newline$ (C) $\frac{2}{\sqrt{x}}$ $\newline$ (D) $\frac{1}{2 \sqrt{4 x+1}}$

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Math Problems

Algebra 2

Simplify variable expressions using properties

Full solution

y=\sqrt{4 x+1}

\newline

\frac{d y}{d x}=?

\newline

Choose

1

answer:

\newline

(A)

\frac{2}{\sqrt{4 x+1}}

\newline

(B)

2 \sqrt{4 x+1}

\newline

(C)

\frac{2}{\sqrt{x}}

\newline

(D)

\frac{1}{2 \sqrt{4 x+1}}

Apply Chain Rule: To find the derivative of $y$ with respect to $x$ , we will use the chain rule. The chain rule states that the derivative of a composite function is the derivative of the outer function evaluated at the inner function times the derivative of the inner function.
Identify Outer and Inner Functions: The outer function is the square root function, and the inner function is $(4x+1)$ . The derivative of the outer function, $\sqrt{u}$ , with respect to $u$ is $(1/2)\sqrt{u}$ . The derivative of the inner function, $4x+1$ , with respect to $x$ is $4$ .
Calculate Derivative: Applying the chain rule, we multiply the derivative of the outer function by the derivative of the inner function. This gives us $(\frac{1}{2})\sqrt{4x+1} \times 4$ .
Simplify Expression: Simplify the expression by multiplying $(\frac{1}{2})$ by $4$ , which gives us $2$ . So the derivative is $\frac{2}{\sqrt{4x+1}}$ .