"Compute the given partial derivatives. f(x,y)=3x2y+4x3y2−7xy5,fx(1,2)" was answered by students like you

Tiffany Russell

Answered question

2022-01-14

Compute the given partial derivatives.

f (x, y) = 3 x^{2} y + 4 x^{3} y^{2} - 7 x y^{5}, f_{x} (1, 2)

eskalopit

Beginner2022-01-15Added 31 answers

Step 1
Given,

f (x, y) = 3 x^{2} y + 4 x^{3} y^{2} - 7 x y^{5}, f_{x} (1, 2)

The objective is to determine the partial derivatives

f_{x}

of the given function at given point.
For partial differentiation, differentiate the given function with respect to x, taking y as a constant.
Step 2

f_{x} = \frac{\partial}{\partial x} (3 x^{2} y + 4 x^{3} y^{2} - 7 x y^{5})

= \frac{\partial}{\partial x} (3 x^{2} y) + \frac{\partial}{\partial x} (4 x^{3} y^{2}) - \frac{\partial}{\partial x} (7 x y^{5})

= 6 y x + 12 y^{2} x^{2} - 7 y^{5}

Thus, the value of

f_{x}

at (1,2) is,

f_{x} (1, 2) = 6 y x + 12 y^{2} x^{2} - 7 y^{5}

= 6 (2) (1) + 12 {(2)}^{2} {(1)}^{2} - 7 {(2)}^{5}

= 6 (2) (1) + 12 \cdot 4 {(1)}^{2} - 7 {(2)}^{5}

=12+12*4*1-7*32
=12+48-224
=-164

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