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Find the derivative of the following functions.$$y=5 x^{2}+\cos x$$

Calculus 1 / AB

Chapter 3

Derivatives

Section 5

Derivatives of Trigonometric Functions

Differentiation

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we are looking for The derivative of y is equal to five x squared plus Co sign of X to know Tate that we want a derivative. It'll look like D over DX of why is equal to D over DX of five X squared plus Co. Sign of X instead of using an D x D over DX of why you can also do Why prime Too short and your notation So now we are looking for the derivative of five X squared plus coastline X D over DX of five X squared plus coastline elex. To find this, we want to use the some difference rule to break apart the derivatives that will look like F plus minus. G prime is equal to F prime plus minus G prime. Already. To break this down, it'll look like D over DX of five X squared plus D over DX of CO Sign X. We're first going to look for our five x squared D over DX of five X squared. That will be done first when you take out the constant so it'll look like five over D over DX of X squared to find the derivative of X squared. We're going to use the power rule D over DX of X to the A A in this case is, too, that is equal to a Times X to the A minus one. This will look like five times two x to the Tu minus one, which is 10 X. Our next derivative is D over DX of CO sign of X, which is a negative sign of X. Let's put this all together. Are y prime is equal Teoh 10 x minus Sign of X instead of using why prime, you can also do d over DX of why is equal to 10 x minus sign of X.

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