calculus 1

posted by .

Please help !!!!!
Find dy/dx by implicit differentiation.
(sin πx + cos πy)4 = 65

• calculus 1 -

I assume that the 4 is an exponent, and you mean
(sin ðx + cos ðy)^4 = 65
Differentiate both sides of the equation with respect to x.
4 (sin ðx + cos ðy)^3 *d/dx[sin ðx + cos ðy] = 0
[sin(pi*x) + cos(pi*y)]^3 * [(pi*cos(pi*x) - pi*sin(pi*y)*(dy/dx)] = 0
You can divide out the first [ ] term on the left. Only second [] term can be zero.
(pi*cos(pi*x) = pi*sin(pi*y)*dy/dx
dy/dx = (1/pi)cot(pi*y)

• calculus 1 -

(pi*cos(pi*x) = pi*sin(pi*y)*dy/dx
dy/dx = (1/pi)cot(pi*y)
I think the pi should be canceled, and the term cos and sin can not be identified as cot, because it is cos of x, and sin of y.
Is it right?

• calculus 1 -

pi can be cancelled, and yes, your are right about the cot.
Thank you for your alert corrections

• calculus 1 -

So, What do u think how we solve this? :)

Respond to this Question

 First Name School Subject Your Answer

Similar Questions

1. Math

Evaluate *Note - We have to find the exact value of these. That I know to do. For example sin5π/12 will be broken into sin (π/6) + (π/4) So... sin 5π/12 sin (π/6) + (π/4) sin π/6 cos π/4 + cos …
2. Math 2nd question

Express as a single sine or cosine function (note: this is using double angle formulas) g) 8sin^2x-4 I just don't get this one. I know it's got something to do with the 1-2sin^2x double angle formula. It's the opposite though?
3. Math integrals

What is the indefinite integral of ∫ [sin (π/x)]/ x^2] dx ?
4. Precalculus

Use one of the identities cos(t + 2πk) = cos t or sin(t + 2πk) = sin t to evaluate each expression. (Enter your answers in exact form.) (a) sin(19π/4) (b) sin(−19π/4) (c) cos(11π) (d) cos(53π/4) …
5. Trig Help!

Question: Trying to find cos π/12, if cos π/6 = square root 3 over 2, how to find cos π/12 using DOUBLE angle formula?
6. product of function

Given: f(x)=2 cos x and g(x)=sin x. Which of these expressions is equivalent to (fxg)(π/16)?
7. TRIGONOMETRY

Can you check my work, please? This is for a trig study guide for my final next week. I'd like to know if I'm doing this right. :) 2. The polar coordinates of a point are given. Find the rectangular coordinates of each point. a. (5,(π
8. Calculus

(cos πx + sin πy)4 = 54; Implicit Differentation
9. Math, please help

Which of the following are trigonometric identities?
10. precalc

Given that sec 3π/10 ≈ 17/10 and csc 3π/10 ≈ 17/14, find the following: 1. sin 3π/10 ≈ 14/17 (is this one correct) 2. csc 43π/10 ≈ 3. sec 2π/10 ≈ 4. cot -12π/10 ≈ 5. …

More Similar Questions