Friday

November 21, 2014

November 21, 2014

Posted by **john** on Friday, October 15, 2010 at 12:06am.

Find dy/dx by implicit differentiation.

(sin πx + cos πy)4 = 65

- calculus 1 -
**drwls**, Friday, October 15, 2010 at 6:04amI 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 -
**john**, Friday, October 15, 2010 at 11:08am(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 -
**drwls**, Friday, October 15, 2010 at 12:06pmpi can be cancelled, and yes, your are right about the cot.

Thank you for your alert corrections

- calculus 1 -
**Matt**, Friday, October 15, 2010 at 12:10pmSo, What do u think how we solve this? :)

**Answer this Question**

**Related Questions**

Trig Help! - Question: Trying to find cos π/12, if cos π/6 = square ...

Math, please help - Which of the following are trigonometric identities? (Can be...

Math - Evaluate *Note - We have to find the exact value of these. That I know to...

Math integrals - What is the indefinite integral of ∫ [sin (π/x)]/ x^...

Precalculus - Use one of the identities cos(t + 2πk) = cos t or sin(t + 2&#...

product of function - Given: f(x)=2 cos x and g(x)=sin x. Which of these ...

TRIGONOMETRY - Can you check my work, please? This is for a trig study guide for...

Calculus - (cos πx + sin πy)4 = 54; Implicit Differentation

Math 2nd question - Express as a single sine or cosine function (note: this is ...

Math help again - cos(3π/4+x) + sin (3π/4 -x) = 0 = cos(3π/4)cosx...