Find y'' for the following functions.
y = tan x

Question

Find y'' for the following functions.

y = tan x

Accepted Answer

Welcome back, everyone. In this problem, we want to find a second derivative Y for the function Y equals 25 multiplied by the cotangent of X. A says it's negative 50 2 X X. B 25 2 X X. C. 50 co squared X, X, and D 25 core X X. Now, to find the second derivative for the function, what that basically means is that we're just going to differentiate Y twice. So let's find the first derivative and differentiate it again to get the second derivative. Now, given Y equals 25 multiplied by the cotangent of X, recall, OK, that the derivative of the cotangent. OK, of X. Is equal to negative cos X2 X, OK. So with that in mind then that means. Now the first derivative of Y is going to be equal to 25 multiplied by negative core x or negative 25 co2X. So we have our first derivative. Next, let's try to find the second derivative. That means we're going to differentiate Y. So now differentiating Y differentiating our first derivative here. Notice that this derivative or this term. To differentiate this term, we'd need to use the chain rule because it has an, it, it's a composite function, right? Now remember that to use the chain rule, basically. We're going to first bring down our power, OK. So that means we're gonna have two multiplied by our term subtracting one from the poor. OK. So, if I were to have our term here, so that's gonna be uh negative, well, we still have our 25. So now it's gonna be 2 multiplied by the core of X to the power of 2 minus 1, multiplied by the derivative of our inner function. So that is. The derivative of the core kind of X. So now the question is, how do we differentiate the coresequant? Well, recall that the derivative of the coresant is equal to negative co X multiplied by X. So if we apply that idea here, that's gonna be -25 multiplied by 2 negative 50, multiplied by the co-sequant of X rates to the core of 1, or we can just write cosack X, multiplied, OK, by negative co X X. The derivative of the cosicant of X. And now if we simplify this expression here, negative multiplied by negative will be positive. So this will be 50 multiplied by the core C square of X. OK, these two terms are multiplied, multiplied by the cotangent of X. Thus, the second derivative of Y is 50 co 2 X X. If we look back at our answer twice, that tells us that C is the correct answer. Thanks a lot for watching everyone. I hope this video helped.

Find y'' for the following functions.
y = tan x

Key Concepts

Second Derivative

Differentiation Rules

Trigonometric Derivatives

Watch next

Find y'' for the following functions.y = tan x

Key Concepts

Second Derivative

Differentiation Rules

Trigonometric Derivatives

Watch next

Find y'' for the following functions.
y = tan x