Consider the following. $3x^4 + y^5 = 8x$ (a) Find $y'$ by implicit differentiation. $y' = \frac{3x}{y}$ (b) Solve the equation explicitly for $y$ and differentiate to get $y'$ in terms of $x$. $y' = \frac{3x}{(3x^2 - 8)^{(\frac{1}{2})}}$ (c) Check that your solutions to parts (a) and (b) are consistent by substituting the expression for $y$ into your solution f $y' = -\frac{1}{(3x - 1)^5}$
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Differentiating both sides of the equation 3x^4 + y^5 = 8x with respect to x, we get: 12x^3 + 5y^4 * y' = 8. Show more…
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