13-26 Implicit differentiation Carry out the following steps.

Question

b. Find the slope of the curve at the given point.

sin y = 5x⁴−5; (1, π)

Accepted Answer

Welcome back, everyone. Given the equation cosine of Y equals x cubed plus 2 X, use implicit differentiation to find the slope of the tangent line at the 0.5 divided by 2. We're given 4 answer choices A says -2, B says 2, C says 4, and D says -4. So to find the slope of the tangent line at the given point, we have to identify the derivative of Y at a point X Y to begin with, right? And then we're going to substitute the given point into the expression to evaluate the value of the slope of the tension line. So let's analyze the given equation. And let's apply implicit differentiation, which means that we have to take the derivative of the left hand side and set it equal to the derivative of the right hand side. So the derivative of cosine of y must be equal to the derivative of X cubed plus 2 X. On the left we have to differentiate cosine of Y. The derivative of cosine is a negative sign, so we get negative sign of Y. And because we have a composite function, Y is not an independent variable, it is a function, we have to apply the chain rule and multiply by Y. And this must be equal to 3 x 2, which is the derivative of X cubed based on the power rule, plus 2 multiplied by x derivative, which is 2 once again applying the power rule. So we now solve for Y and we get Y equals. We x2 + 2 divided by a negative sign of Y we can factor out the negative sign. And say that we are dividing by sign of y because the negative sign is now in front of the fraction. And we want to evaluate Y at x equals 0 Y equals pi divided by 2. So let's clearly state that we have X of 0, we have Y of pi divided by 2. So we want to substitute these values into the expression. So we get negative 3 multiplied by 0 squared + 2 divided by sin. Off 5 divided by 2. Which gives us negative. In the numerator we get 0 + 2. That's 2. In the denominator we have 1, so -2 divided by 1 gives us -2, which corresponds to the answer choice A. Thank you for watching.

13-26 Implicit differentiation Carry out the following steps.b. Find the slope of the curve at the given point.sin y = 5x⁴−5; (1, π)

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13-26 Implicit differentiation Carry out the following steps.
b. Find the slope of the curve at the given point.
sin y = 5x⁴−5; (1, π)