Problem

Find the partial derivative of the dependent vari…

Problem 6 Easy Difficulty

Find the partial derivative of the dependent variable or function with respect to each of the independent variables.
$$z=\cos 2 x+y^{3}$$

Answer

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Calculus 3

Basic Technical Mathematics with Calculus

Chapter 29

Partial Derivatives and Double Integrals

Section 3

Partial Derivatives

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Video Transcript

All right. We want to find the first partial derivatives of the function F of X. Y is equal to the co sign of two X plus Y. Que This question is challenging understanding of derivatives not only from the perspective of single variable calculus, what we've already learned, but also understanding of how to take partial derivatives in multi variant function. So we are looking for the two first partial derivatives, DfX and DFD. Why we use standard differentiation techniques when taking each. So when we take the F D X, we take it as a normal standard X derivative where every Y terms of constant and when we take the FBI we treat every extreme is a constant. So for instance, when we take Fx for cossacks to to expose why cute coaster X will be differentiated but white you will go to zero as a constant. So F X is negative to sign two X trig and metric chain rule in khost two X plus zero. As we mentioned or negative to sign two X, then f y is zero because Coast Director the constant plus three white square the power rule. Given final solution, f Y equals three y squared.

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