Expert Answer to "Find all first partial derivatives. f(x,y)=5x3+7y−3"

College
Calculus and Analysis
Differential Calculus
Derivatives

slaggingV

Answered question

2021-02-25

Find all first partial derivatives.

f (x, y) = 5 x^{3} + 7 y - 3

Answer & Explanation

svartmaleJ

Skilled2021-02-26Added 92 answers

Step 1
Given:
First partial derivation, $f (x, y) = 5 x^{3} + 7 y - 3$
Find all first partial derivatives,
$f_{x} = \frac{\partial f}{\partial x}$
$= 15 x^{2} + 0 - 0$
$= 15 x^{2}$
$f_{y} = \frac{\partial f}{\partial y}$
$= 0 + 7 - 0 = 7$
Step 2
$f_{x x} = \frac{\partial}{\partial x} (\frac{\partial f}{\partial x})$
$= \frac{\partial}{\partial x} (15 x^{2}) = 30 x$

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