Keith S. answered • 08/24/20

PhD Student & Tutor Specializing in Middle School to High School Math

Eric B.

asked • 08/24/20
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Keith S. answered • 08/24/20

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PhD Student & Tutor Specializing in Middle School to High School Math

Dr. Andy T. answered • 08/24/20

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UT Austin Ph.D. in Physics and Certified Math Teacher at Top STEM HS

Hi Eric,

You can find dy/dx using implicit differentiation. This allows us to solve for dy/dx without needing to first solve for y (sometimes it might even be impossible to solve for y). Simply differentiate each side with respect to x, and use the chain rule whenever you encounter y, recalling that y is some function of x. Doing so gives

d/dx cos(4x-y) = d/dx (x+y)

-sin(4x-y) d/dx(4x-y) = 1 + dy/dx

-sin(4x-y) (4-dy/dx) = 1 + dy/dx

-4sin(4x-y)+sin(4x-y)dy/dx = 1 + dy/dx

sin(4x-y)dy/dx - dy/dx = 1 + 4sin(4x-y)

dy/dx (sin(4x-y) - 1) = 1 + 4sin(4x-y)

dy/dx = (1 + 4sin(4x-y))/(sin(4x-y) - 1).

I hope that helps!

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