Thread: Partial Derivatives

Could someone show me where to go at ??? please

dz/dx is representing partial z with respect to x.

Find the value of dz/dx at the point (1,1,1) if the equation

xy+(z^3)x-2yz=0

defines z as a function of the two independent variables x and y and the partial derivative.

so we need to differentiate with respect to x?

d/dx(xz) + d/dx((z^3)x)-d/dx(2yz) = 0

x dz/dx + ??? - 2y dz/dx = 0

Originally Posted by ur5pointos2slo

Could someone show me where to go at ??? please

dz/dx is representing partial z with respect to x.

Find the value of dz/dx at the point (1,1,1) if the equation

xy+(z^3)x-2yz=0

defines z as a function of the two independent variables x and y and the partial derivative.

so we need to differentiate with respect to x?

d/dx(xz) + d/dx((z^3)x)-d/dx(2yz) = 0

x dz/dx + ??? - 2y dz/dx = 0

Yes, you partially differentiate both sides of the equation with respect to x.



Now since , we use the product rule to evaluate :



In the case of , we just have since y is a constant and z depends on x.

Thus, it follows that we have

Does this make sense?

That makes sense. Thank you.