Homework Help is Here – Start Your Trial Now!
Math
Advanced Math
A function is defined impilcitly by the equations. 7y2+6x3 Cos(x4y²) - 4 ln(y+5)= 65+ (x³ +7)³ a. Find an expression for at the point (x,y). dx b. Using Part (a) evaluate the derivative at the Point (-2,-4).

A function is defined impilcitly by the equations. 7y2+6x3 Cos(x4y²) - 4 ln(y+5)= 65+ (x³ +7)³ a. Find an expression for at the point (x,y). dx b. Using Part (a) evaluate the derivative at the Point (-2,-4).

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
See similar textbooks
icon
Related questions
Question
100%
Question A function is defined impilcitly by the equations. 7y2+6x3 Cos(x - y²) - 4 ln(y + 5) = 65+ (x³ +7)³ a. Find an expression for at the point (x,y). dx b. Using Part (a) evaluate the derivative at the Point (-2,-4).
Transcribed Image Text:Question A function is defined impilcitly by the equations. 7y2+6x3 Cos(x - y²) - 4 ln(y + 5) = 65+ (x³ +7)³ a. Find an expression for at the point (x,y). dx b. Using Part (a) evaluate the derivative at the Point (-2,-4).
Expert Solution
steps

Step by step

Solved in 4 steps with 13 images

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Follow-up Questions
Read through expert solutions to related follow-up questions below.
Follow-up Question

Hi,

I believe you may have forgotten to multiply 3x^2cos(x^4-y^2) by the 6?

Giving 18x^2cos(c^4-y^2)

See highlighted in image

Step 2: Calculation: (a) Given the equations: 7y² + 6x³ cos(x² - y²) - 4 ln (y+5)=65+ (x²¾+7) 3 Differentiating both sides of w.n.tex' we get dx [74 276 x ³ cos(x 4-y²)-4(y+5)] = [65+ (x²=7)³] >7.0 (y²)+6.x (x² cos(x 2 y 3) -4.2x (In(y+5)) dx = 0x (65) + ((x²+7)³) dx dx 7.24d/ +6 [x³ (cos(x²¼ y³) + cos(x²±43). ox (x3)] dx - dx dx · 4. 115 3 x ( 1 + 5) = 0 + 3(x² + 7)² (x²¾7) y+5 dy dx ⇒ 14y diy / +6 [x³ (-sin(x² y²). (4x²-24 1/2) + cos(x²-4³)-3x²) dy dx - 4 (3/2+0) = 3(x+7)²= (3x²+0) >14 y d²/ +6 [ -x³sin (x²≤ y²) (4x³ 2 ydy 1) + 3x cos(x²yz)] dx 2 - 4 dy = 9x² (x²³+7)² y+52x → 144 dy - 24 x 6 sin(x²-43) +122³y dy sin(x²-42) dy-24x6sinlay)+1225y +3x² cos(x² - y²) - 4 dy = 9x² (x²+7)² 4+5x dy [144 +12x³ y sin (x²1 y2) - 45] dy = → कट -- y+5] 24x6 Sin (x²-42) -3x² cos(x²¼ y²) +9x² (x²³+7)² 24x6 sin(x-2)-3x² cos(x²+ y²)+9x² (x³+7)² 144 +12x³ y sin (x 4_42) - 4 y+5 (b)[22] - 24(-2) 6 sin (0) -3(-2)²-c05(0)+3(-2)² (-8 +7) 2 = Tat(-254) 1 = Կ 14(-4)+12 (2)³ (-4) Sin (0) - 4/4+5 0-12 (1) +9 (4)(-1)² -56+0- -12+36(1) -12+36 24 -56-4 - во .60 = #P Solution (a) dy - 24x6 sin(x4y²) -3x²-COS (x²-4²) +9x² (x³+7)2 dx = 144 +12x³y sin(x4_43) - 45 4+5
Transcribed Image Text:Step 2: Calculation: (a) Given the equations: 7y² + 6x³ cos(x² - y²) - 4 ln (y+5)=65+ (x²¾+7) 3 Differentiating both sides of w.n.tex' we get dx [74 276 x ³ cos(x 4-y²)-4(y+5)] = [65+ (x²=7)³] >7.0 (y²)+6.x (x² cos(x 2 y 3) -4.2x (In(y+5)) dx = 0x (65) + ((x²+7)³) dx dx 7.24d/ +6 [x³ (cos(x²¼ y³) + cos(x²±43). ox (x3)] dx - dx dx · 4. 115 3 x ( 1 + 5) = 0 + 3(x² + 7)² (x²¾7) y+5 dy dx ⇒ 14y diy / +6 [x³ (-sin(x² y²). (4x²-24 1/2) + cos(x²-4³)-3x²) dy dx - 4 (3/2+0) = 3(x+7)²= (3x²+0) >14 y d²/ +6 [ -x³sin (x²≤ y²) (4x³ 2 ydy 1) + 3x cos(x²yz)] dx 2 - 4 dy = 9x² (x²³+7)² y+52x → 144 dy - 24 x 6 sin(x²-43) +122³y dy sin(x²-42) dy-24x6sinlay)+1225y +3x² cos(x² - y²) - 4 dy = 9x² (x²+7)² 4+5x dy [144 +12x³ y sin (x²1 y2) - 45] dy = → कट -- y+5] 24x6 Sin (x²-42) -3x² cos(x²¼ y²) +9x² (x²³+7)² 24x6 sin(x-2)-3x² cos(x²+ y²)+9x² (x³+7)² 144 +12x³ y sin (x 4_42) - 4 y+5 (b)[22] - 24(-2) 6 sin (0) -3(-2)²-c05(0)+3(-2)² (-8 +7) 2 = Tat(-254) 1 = Կ 14(-4)+12 (2)³ (-4) Sin (0) - 4/4+5 0-12 (1) +9 (4)(-1)² -56+0- -12+36(1) -12+36 24 -56-4 - во .60 = #P Solution (a) dy - 24x6 sin(x4y²) -3x²-COS (x²-4²) +9x² (x³+7)2 dx = 144 +12x³y sin(x4_43) - 45 4+5
Solution
Bartleby Expert
SEE SOLUTION
Follow-up Question

From line 2 to 3 (in step 2 calculations) where did the 6 go for 6 d/dx [x^3cos(x^4-y^2)]

7[2] + [x³- 3 dx d 7y²+6 [r³cos(x²— y²)] − 4——|_ ln(y+5) = 7|2y dy dx dx d - d d d 4. 65+ dx dx +7)³ 3 dx -cos(x4 - y²) + cos(x4 — y²). d 1 dy -x· 4. dx (y+5) dx ·=0+ 3(x³ +7) ²(3x²)
Transcribed Image Text:7[2] + [x³- 3 dx d 7y²+6 [r³cos(x²— y²)] − 4——|_ ln(y+5) = 7|2y dy dx dx d - d d d 4. 65+ dx dx +7)³ 3 dx -cos(x4 - y²) + cos(x4 — y²). d 1 dy -x· 4. dx (y+5) dx ·=0+ 3(x³ +7) ²(3x²)
Solution
Bartleby Expert
SEE SOLUTION
Recommended textbooks for you
Advanced Engineering Mathematics
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
Basic Technical Mathematics
Basic Technical Mathematics
Advanced Math
ISBN:
9780134437705
Author:
Washington
Publisher:
PEARSON
Topology
Topology
Advanced Math
ISBN:
9780134689517
Author:
Munkres, James R.
Publisher:
Pearson,
SEE MORE TEXTBOOKS