Question

Consider the following. $8x^2 - y^5 = 7$ (a) Find $y'$ by implicit differentiation. $y' = \frac{16x}{5y^4}$ (b) Solve the equation explicitly for $y$ and differentiate to get $y'$ in terms o $y' = \frac{16x}{5y \sqrt[5]{8x^2 - 7}^4}$ (c) Check that your solutions to parts (a) and (b) are consistent by substi (a). $y' = \text{verified}$ Need Help? Read It

          Consider the following.
$8x^2 - y^5 = 7$
(a) Find $y'$ by implicit differentiation.
$y' = \frac{16x}{5y^4}$
(b) Solve the equation explicitly for $y$ and differentiate to get $y'$ in terms o
$y' = \frac{16x}{5y \sqrt[5]{8x^2 - 7}^4}$
(c) Check that your solutions to parts (a) and (b) are consistent by substi
(a).
$y' = \text{verified}$
Need Help? Read It

Consider the following.
8x^2 - y^5 = 7
(a) Find y' by implicit differentiation.
y' = (16x)/(5y^4)
(b) Solve the equation explicitly for y and differentiate to get y' in terms o
y' = (16x)/(5y √(8x^2 - 7)^4)
(c) Check that your solutions to parts (a) and (b) are consistent by substi
(a).
y' = verified
Need Help? Read It

Added by Antonia B.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Vishva S

02/24/2022

Step 1

To find y', we need to differentiate both sides of the equation with respect to x. Differentiating 8x^2 - y^5 = 7 with respect to x, we get: 16x - 5y^4 * y' = 0 Show more…

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Texts: corrected Consider the following: 8x^2 - y^5 = 7 (a) Find y' by implicit differentiation. 16x - 5y^4 * y' = 0 (b) Solve the equation explicitly for y and differentiate to get y' in terms of x. y = (8x^2 - 7)^(1/5) y' = (1/5) * (8x^2 - 7)^(-4/5) * 16x (c) Check that your solutions to parts (a) and (b) are consistent by substituting y and y' into the original equation. Verified. X Need Help? Read It