13-26 Implicit differentiation Carry out the following steps.

Question

a. Use implicit differentiation to find dy/dx.

sin y = 5x⁴−5; (1, π)

Accepted Answer

Welcome back, everyone. Given the equation cosine of Y equals x cubed + 2 X, use implicit differentiation to find the first derivative. We're given 4 answer choices as as negative, 3 X2 + 2 divided by. Cosine of Y. B says -3 x2 + 2 divided by sin of y. C says 3x2 + 2 divided by sin of y, and D says 3x2 + 2 divided by cosine of y. So we're going to use implicit differentiation, and this means that we want to differentiate the left hand sides, we're taking the derivative of cosine of Y and setting it equal to the derivative of the right hand side. So the derivative of X cubed plus 2 X. Now let's begin with the derivative of the left hand side. We have to recall that the derivative of cosine of X is negatives of X. So in this case we get negative sign of Y, but because we don't have X, we have Y, which is a function, right? We have to apply the chain rules, so we have to multiply by Y. On the right hand side we have to apply the power rule. It says that the derivative of X to the power of N is N. X raises the power of n minus 1. So the derivative of X cubed is going to be 3. We bring down the exponent and we decrease the original exponent by 1 unit. So 3 x2 plus. 2 multiplied by 1, right? So essentially we, we can factor out the constant 2, and the derivative of X is just 1 based on the same rule. So now let's solve for Y because our goal is to find the first derivative, and we have to take 3 X2 + 2 and divide that by negative sign of Y and that's it. From here we can just factor out the negative sign, and we're going to get negative 3 X2 + 2 divided by sin of y. Which is D Y divided by D X or the first derivative. What can we conclude? Well, we can conclude that the correct answer to this problem corresponds to the answer choice B. Thank you for watching.

13-26 Implicit differentiation Carry out the following steps.a. Use implicit differentiation to find dy/dx.sin y = 5x⁴−5; (1, π)

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13-26 Implicit differentiation Carry out the following steps.
a. Use implicit differentiation to find dy/dx.
sin y = 5x⁴−5; (1, π)