differentiate Y=(3x+8) ^1/3
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Find dy/dx y^2+3x=8
y2+3x=8y2+3x=8
Differentiate both sides of the equation.
ddx(y2+3x)=ddx(8)ddx(y2+3x)=ddx(8)
Differentiate the left side of the equation.
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2yddx[y]+32yddx[y]+3
Since 88 is constant with respect to xx, the derivative of 88 with respect to xx is 00.
00
Reform the equation by setting the left side equal to the right side.
2yy'+3=02yy′+3=0
Solve for y'y′.
y'=−32yy′=-32y
Replace y'y′ with dydxdydx.
dydx=−32y
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