Find y⁽⁴⁾ = d⁴y/dx⁴ if:

b. y = 9 cos x

Question

Find y⁽⁴⁾ = d⁴y/dx⁴ if:

b. y = 9 cos x

Accepted Answer

Welcome back, everyone. Calculate the fifth derivative of the function F of X equals 17 off x. We're given 4 answer choices A -17 cosine of X, B 17 sin off X, C 17 cosine of X, and D-17s off X. So, for this problem, we will need two formulas, the derivative of sine of X is, cosine of X based on the table of basic derivatives, and the derivative of cosine of X. Is going to be equal to negative sign of X. If we want to identify the 5th derivative of the function. This means that we will start with the first derivative and identify. The second derivative and so on until we reach the 5th derivative, right? So let's begin with the first derivative F of X. We can factor out the constant, which is 17, and simply differentiate sine of X. We know that sine of X is cosine, so we get 17 cosine of X. That's our first derivative. Now, the second derivative is simply the derivative of the first derivative, so we want to take the answer from the previous part, 17 cosine of X, and we want to differentiate that. Once again we are factoring out 17, and the derivative of cosine is negative sign, so we get -17 of X for the second derivative. For the third derivative, we want to differentiate the previous answer, so we're taking the derivative of -17 of x. -17 is a constant so we're factoring it out in the derivative of sine as cosine. Let's move on to the 4th derivative. Which means that we're taking the derivative of -17 cosine of X. The derivative of cosine is negative sign. So negative sign multiplied by -17 gives us a positive number, which is 17 of X. And finally, the 5th derivative is the derivative. Of 17 of X or basically the first derivative, right? Because we have previously differentiated F of X, which was 17 multiplied by sin of x, so we can just rewrite it as the first derivative, and that's 17 cosine of X. So the correct answer to this problem corresponds to the answer choice C. 17 cosine off x. Thank you for watching.

Find y⁽⁴⁾ = d⁴y/dx⁴ if:

b. y = 9 cos x

Key Concepts

Higher-Order Derivatives

Trigonometric Functions

Derivative Rules

Watch next

Find y⁽⁴⁾ = d⁴y/dx⁴ if:b. y = 9 cos x

Key Concepts

Higher-Order Derivatives

Trigonometric Functions

Derivative Rules

Watch next

Find y⁽⁴⁾ = d⁴y/dx⁴ if:

b. y = 9 cos x