Check the solution to "Find the indicated derivatives dsdt if s=t4t+9" - Plainmath

permaneceerc

Answered question

2021-09-15

Find the indicated derivatives

\frac{d s}{d t} if s = \frac{t}{4 t + 9}

Answer & Explanation

jlo2niT

Skilled2021-09-16Added 96 answers

Step 1
The given function is

s = \frac{t}{4 t + 9}

.
The derivative

\frac{d s}{d t}

is obtained using the formula

{(\frac{u}{v})}^{'} = \frac{v u^{'} - u v^{'}}{v^{2}}

Step 2
Now the derivative

\frac{d s}{d t}

is obtained as follows.

\frac{d s}{d t} = \frac{d}{d t} (\frac{t}{4 t + 9})

= \frac{(4 t + 9) \frac{d}{d t} (t) - t \frac{d}{d t} (4 t + 9)}{{(4 t + 9)}^{2}}

= \frac{4 t + 9 (1) - t (4)}{{(4 t + 9)}^{2}} (∵ \frac{d}{d x} (x^{n}) = n x^{n - 1})

= \frac{4 t + 9 - 4 t}{{(4 t + 9)}^{2}}

= \frac{9}{{(4 t + 9)}^{2}}

Jeffrey Jordon

Expert2022-02-01Added 2605 answers

Answer is given below (on video)

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?