Question

Найти dz/dx если z=3x2y2-7sinx+5cosy-1

Answer 1

$z=3x^2y^2-7sinx+5cosy-1\\\\ \frac{\partial z}{\partial x}=3y^2\cdot 2x-7\, cosx+0-0=6xy^2-7\, cosx$

Answer 2

To find dz/dx, we need to take the partial derivative of the given function z with respect to x while treating y as a constant. Let's proceed step by step.

Given function: z = 3x^2y^2 - 7sin(x) + 5cos(y) - 1

Step 1: Find the derivative of the first term with respect to x. d/dx (3x^2y^2) = 6xy^2

Step 2: Find the derivative of the second term with respect to x. d/dx (-7sin(x)) = -7cos(x)

Step 3: The last two terms are constants, so their derivatives with respect to x will be zero.

Now, let's combine all the results from steps 1 to 3:

dz/dx = 6xy^2 - 7cos(x)

That's the derivative of z with respect to x.