Question

The tricky part about the product rule is remembering to use it. f(x)g(x) = f(x)g'(x) + f'(x)g(x) k(x,y) = x^(2)sin(5x+4y) k_x(x,y) = x^(2)5*cos(5x+4y) + 2xsin(5x+4y) = 5x^(2)cos(5x+4y) + 2xsin(5x+4y) k_y(x,y) = x^(2)4cos(5x+4y) + x^(2)sin(5x+4y) = 4x^(2)cos(5x+4y) + x^(2)sin(5x+4y) g(x,y) = 3y^(2)e^(2x^(4)) g_x(x,y) = 3y^(2)8x^(3)e^(2x^(4)) h(x,y) = xe^(5x^(2)+2y) h_x(x,y) = x10x(e^(5x^(2)+2y)) + e^(5x^(2)+2y)(1) = 10x^(2)e^(5x^(2)+2y) + e^(5x^(2)+2y)

Name: the tricky part about the product rule is remembering to use it fxgx fxgx fxgx kxy x2sin5x4y kxxy x25cos5x4y 2xsin5x4y 5x2cos5x4y 2xsin5x4y kyxy x24cos5x4y x2sin5x4y 4x2cos5x4y x2sin5x4y g 40324
Uploaded: 2019-06-10T17:48:33-08:00
Duration: 1 min 1 s
Channel: Bahar Tehranipoor
Description: the tricky part about the product rule is remembering to use it fxgx fxgx fxgx kxy x2sin5x4y kxxy x25cos5x4y 2xsin5x4y 5x2cos5x4y 2xsin5x4y kyxy x24cos5x4y x2sin5x4y 4x2cos5x4y x2sin5x4y g 40324

          The tricky part about the product rule is remembering to use it. f(x)*g(x) = f(x)g'(x) + f'(x)g(x)

k(x,y) = x^(2)sin(5x+4y)
k_x(x,y) = x^(2)*5*cos(5x+4y) + 2xsin(5x+4y)
= 5x^(2)cos(5x+4y) + 2xsin(5x+4y)
k_y(x,y) = x^(2)*4*cos(5x+4y) + x^(2)sin(5x+4y)
= 4x^(2)cos(5x+4y) + x^(2)sin(5x+4y)

g(x,y) = 3y^(2)e^(2x^(4))
g_x(x,y) = 3y^(2)*8x^(3)e^(2x^(4))

h(x,y) = xe^(5x^(2)+2y)
h_x(x,y) = x*10x(e^(5x^(2)+2y)) + e^(5x^(2)+2y)(1)
= 10x^(2)e^(5x^(2)+2y) + e^(5x^(2)+2y)

the tricky part about the product rule is remembering to use it fxgx fxgx fxgx kxy x2sin5x4y kxxy x25cos5x4y 2xsin5x4y 5x2cos5x4y 2xsin5x4y kyxy x24cos5x4y x2sin5x4y 4x2cos5x4y x2sin5x4y g 40324

Added by Carla R.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Bahar Tehranipoor

06/10/2019

Step 1

Step 1: Given k(x,y) = x^(2)sin(5x+4y), we need to find the partial derivative with respect to x, k_x(x,y). Show more…

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The tricky part about the product rule is remembering to use it. f(x)*g(x) = f(x)g'(x) + f'(x)g(x) k(x,y) = x^(2)sin(5x+4y) k_x(x,y) = x^(2)*5*cos(5x+4y) + 2xsin(5x+4y) = 5x^(2)cos(5x+4y) + 2xsin(5x+4y) k_y(x,y) = x^(2)*4*cos(5x+4y) + x^(2)sin(5x+4y) = 4x^(2)cos(5x+4y) + x^(2)sin(5x+4y) g(x,y) = 3y^(2)e^(2x^(4)) g_x(x,y) = 3y^(2)*8x^(3)e^(2x^(4)) h(x,y) = xe^(5x^(2)+2y) h_x(x,y) = x*10x(e^(5x^(2)+2y)) + e^(5x^(2)+2y)(1) = 10x^(2)e^(5x^(2)+2y) + e^(5x^(2)+2y)