Expert answers to "Find the partial derivatives: f(x,y)=7x7⋅4y3+z3 ∂f∂x=? ∂f∂y=? ∂f∂z=?"

Isa Trevino

Answered question

2021-05-16

Find the partial derivatives:

f (x, y) = 7 x^{7 \cdot 4} y^{3} + z^{3}

\frac{\partial f}{\partial x} =

\frac{\partial f}{\partial y} =

\frac{\partial f}{\partial z} =

Mitchel Aguirre

Skilled2021-05-18Added 94 answers

Step 1
The partial derivatives of function f are given below :
Step 2

f (x, y, z) = 7 \cdot x^{7 \cdot 4} \cdot y^{3} + z^{3}

\frac{\partial f}{\partial x} = \frac{\partial}{\partial x} [7 \cdot x^{7 \cdot 4} \cdot y^{3} + z^{3}]

= 7 (7 \cdot 4) x^{6 \cdot 4} y^{3} = 51 \cdot 8 x^{6 \cdot 4} y^{3}

\frac{\partial f}{\partial y} = \frac{\partial}{\partial y} [7 \cdot x^{7 \cdot 4} \cdot y^{3} + z^{3}] = 27 \cdot x^{7 \cdot 4} y^{2}

\frac{\partial f}{\partial z} = \frac{\partial}{\partial z} [7 \cdot x^{7 \cdot 4} \cdot y^{3} + z^{3}] = 3 z^{2}

Jeffrey Jordon

Expert2022-01-31Added 2605 answers

Answer is given below (on video)

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