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k'(x) = 3x^2 3x^2 Step 4 For the function h(x) = (x^3 - 7)^2 we let k(x) = x^3 - 7 and n = 2 such that h(x) = (k(x))^n. h'(x) = n(k(x))^(n-1)(k'(x)) = 6x^2(x^3 - 7) 6x^2(x^3 - 7) Step 5 We let g(x) = 8x and h(x) = (x^3 - 7)^2. We then determined that g'(x) = 8 and h'(x) = 6x^2(x^3 - 7). f'(x) = (h(x)g'(x) - g(x)h'(x)) / (h(x))^2 = [empty box] SUBMIT SKIP (YOU CANNOT COME BACK) Need Help? Read It SUBMIT ANSWER [2.04/2 Points] Find the derivative of the function. y = -2t / (t + 9)^2 y' = 2(t - 9) / (t + 9)^3 Quick search

          k'(x) = 3x^2
3x^2
Step 4
For the function h(x) = (x^3 - 7)^2 we let k(x) = x^3 - 7 and n = 2 such that h(x) = (k(x))^n.
h'(x) = n(k(x))^(n-1)(k'(x))
= 6x^2(x^3 - 7)
6x^2(x^3 - 7)
Step 5
We let g(x) = 8x and h(x) = (x^3 - 7)^2. We then determined that g'(x) = 8 and h'(x) = 6x^2(x^3 - 7).
f'(x) = (h(x)g'(x) - g(x)h'(x)) / (h(x))^2
= [empty box]
SUBMIT
SKIP (YOU CANNOT COME BACK)
Need Help? Read It
SUBMIT ANSWER
[2.04/2 Points]
Find the derivative of the function.
y = -2t / (t + 9)^2
y' = 2(t - 9) / (t + 9)^3
Quick search

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kx 3x2 3x2 step 4 for the function hx x3 72 we let kx x3 7 and n 2 such that hx kxn hx nkxn 1kx 6x2x3 7 6x2x3 7 step 5 we let gx 8x and hx x3 72 we then determined that gx 8 and hx 6x2x3 7 f 95455

Added by Robert H.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Ma. Theresa Alin

04/29/2024

Step 1

Specifically, $f(x) = g(x) / h(x)$. We are given $g(x) = 8x$ and $h(x) = (x^3 - 7)^2$. We are also given their derivatives: $g'(x) = 8$ and $h'(x) = 6x^2(x^3 - 7)$. The quotient rule for differentiation states that if $f(x) = g(x) / h(x)$, then $f'(x) = Show more…

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k'(x) = 3x^2 3x^2 Step 4 For the function h(x) = (x^3 - 7)^2 we let k(x) = x^3 - 7 and n = 2 such that h(x) = (k(x))^n. h'(x) = n(k(x))^(n-1)(k'(x)) = 6x^2(x^3 - 7) 6x^2(x^3 - 7) Step 5 We let g(x) = 8x and h(x) = (x^3 - 7)^2. We then determined that g'(x) = 8 and h'(x) = 6x^2(x^3 - 7). f'(x) = (h(x)g'(x) - g(x)h'(x)) / (h(x))^2 = [empty box] SUBMIT SKIP (YOU CANNOT COME BACK) Need Help? Read It SUBMIT ANSWER [2.04/2 Points] Find the derivative of the function. y = -2t / (t + 9)^2 y' = 2(t - 9) / (t + 9)^3 Quick search

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