We have an answer to "Find the values of the derivatives ds/dt at..." - Plainmath

Barbara Schroder

Answered question

2021-12-05

Find the values of the derivatives
ds/dt at t=0 if s=2/(4-t)

Answer & Explanation

Aretha Frazier

Beginner2021-12-06Added 16 answers

Step 1
Given function is

s = \frac{2}{4 - t}

s = 2 {(4 - t)}^{- 1}

Differentiating with respect to t, we get

\frac{d s}{d t} = - 2 {(4 - t)}^{- 2} \frac{d}{d t} (4 - t)

\frac{d s}{d t} = - 2 {(4 - t)}^{- 2} (- 1)

\frac{d s}{d t} = \frac{2}{{(4 - t)}^{2}}

Step 2
At t=0, we have

\frac{d s}{d t} = \frac{2}{{(4 - 0)}^{2}}

\frac{d s}{d t} = \frac{2}{16} = \frac{1}{8}

Step 3
Ans: The value of ds/dt at t=0 is 1/8

Do you have a similar question?

Recalculate according to your conditions!

New Questions in Differential Calculus

What is the Mixed Derivative Theorem for mixed second-order partial derivatives? How can it help in calculating partial derivatives of second and higher orders?
How do I find the y-intercept of a parabola?
What are the vertices of $9 x^{2} + 16 y^{2} = 144$ ?
How to determine the rate of change of a function?
Why are the tangents for 90 and 270 degrees undefined?
How to find the center and radius of the circle $x^{2} + y^{2} - 6 x + 8 y = 0$ ?
What is multiplicative inverse of a number?
How to find the continuity of a function on a closed interval?
How do I find the tangent line of a function?
How to find vertical asymptotes using limits?
How to find the center and radius of the circle $x^{2} - 12 x + y^{2} + 4 y + 15 = 0$ ?
Let f be a function so that (below). Which must be true?
I. f is continuous at x=2
II. f is differentiable at x=2
III. The derivative of f is continuous at x=2
(A) I (B) II (C) I and II (D) I and III (E) II and III
How to find the center and radius of the circle given $x^{2} + y^{2} + 8 x - 6 y = 0$ ?
How to find the center and radius of the circle $x^{2} + y^{2} + 4 x - 8 y + 4 = 0$ ?
How to identify the center and radius of the circle ${(x + 3)}^{2} + {(y - 8)}^{2} = 16$ ?

Didn't find what you were looking for?