Question

missed my lecture and need help with this derivative, I tried looking at online resources but I just got confused so if someone could give it to me in that first grade vernacular i would be very appreciative ty <3

Answer 1

Derivative with respect to x: $12x^2y^2-\frac{z^3}{x}+16x^{15}$

Derivative with respect to y: $8x^3y-4e^zy^3+4$

Derivative with respect to z: $-e^z y^4 +\frac{3z^2}{x^2}$

Step-by-step explanation:

We can calculate three derivatives for this function: the derivative with respect to x, the derivative with respect to y, and the derivative with respect to z.

We start with the derivative with respect to x:

$\frac{df}{dx}=4(3x^{3-1})y^2 -0 +z^3(-x^{-1})+0-16x^{16-1}=\\=12x^2y^2-\frac{z^3}{x}+16x^{15}$

Then we calculate the derivative with respect to y:

$\frac{df}{dy}=4x^3(2y^{2-1})-e^z(4y^{4-1})+0+4y^{1-1}=8x^3y-4e^zy^3+4$

Finally, we calculate the derivative with respect to z:

$\frac{df}{dz}=0-e^z y^4 +\frac{3z^{3-1}}{x^2}+0-0=-e^z y^4 +\frac{3z^2}{x^2}$

Learn more about differentiation:

brainly.com/question/4279146

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