Answer:
![\frac{dy}{dx} = \frac{ \cos(x + y)}{[1 - \cos(x + y)] }](https://tex.z-dn.net/?f=%20%5Cfrac%7Bdy%7D%7Bdx%7D%20%20%3D%20%20%5Cfrac%7B%20%5Ccos%28x%20%2B%20y%29%7D%7B%5B1%20-%20%5Ccos%28x%20%2B%20y%29%5D%20%7D%20)
Step-by-step explanation:
Let y = sin(x+y)
Differentiating with respect to x on both sides.
![\frac{dy}{dx} = \frac{d}{dx} \sin(x + y) \\ \\ \frac{dy}{dx} = \cos(x + y)\frac{d}{dx} (x + y) \\ \\ \frac{dy}{dx} = \cos(x + y)(1 + \frac{dy}{dx}) \\ \\ \frac{dy}{dx} = \cos(x + y) +\cos(x + y) \frac{dy}{dx} \\ \\ \frac{dy}{dx} - \cos(x + y) \frac{dy}{dx} = \cos(x + y) \\ \\ \frac{dy}{dx} [1 - \cos(x + y)] = \cos(x + y) \\ \\ \purple {\bold {\frac{dy}{dx} = \frac{ \cos(x + y)}{[1 - \cos(x + y)] }}}](https://tex.z-dn.net/?f=%20%5Cfrac%7Bdy%7D%7Bdx%7D%20%20%3D%20%20%5Cfrac%7Bd%7D%7Bdx%7D%20%20%5Csin%28x%20%2B%20y%29%20%5C%5C%20%20%5C%5C%20%20%5Cfrac%7Bdy%7D%7Bdx%7D%20%20%3D%20%20%5Ccos%28x%20%2B%20y%29%5Cfrac%7Bd%7D%7Bdx%7D%20%20%28x%20%2B%20y%29%20%5C%5C%20%20%5C%5C%20%5Cfrac%7Bdy%7D%7Bdx%7D%20%20%3D%20%20%5Ccos%28x%20%2B%20y%29%281%20%2B%20%5Cfrac%7Bdy%7D%7Bdx%7D%29%20%5C%5C%20%20%5C%5C%20%20%5Cfrac%7Bdy%7D%7Bdx%7D%20%20%3D%20%20%5Ccos%28x%20%2B%20y%29%20%2B%5Ccos%28x%20%2B%20y%29%20%5Cfrac%7Bdy%7D%7Bdx%7D%20%5C%5C%20%20%5C%5C%20%20%5Cfrac%7Bdy%7D%7Bdx%7D%20%20%20-%20%5Ccos%28x%20%2B%20y%29%20%5Cfrac%7Bdy%7D%7Bdx%7D%20%3D%20%20%5Ccos%28x%20%2B%20y%29%20%5C%5C%20%20%5C%5C%20%20%5Cfrac%7Bdy%7D%7Bdx%7D%20%20%5B1%20-%20%5Ccos%28x%20%2B%20y%29%5D%20%3D%20%20%5Ccos%28x%20%2B%20y%29%20%5C%5C%20%20%5C%5C%20%5Cpurple%20%7B%5Cbold%20%7B%5Cfrac%7Bdy%7D%7Bdx%7D%20%20%3D%20%20%5Cfrac%7B%20%5Ccos%28x%20%2B%20y%29%7D%7B%5B1%20-%20%5Ccos%28x%20%2B%20y%29%5D%20%7D%7D%7D%20)
Answer:
Step-by-step explanation:
Answer:
9
Step-by-step explanation:
Answer:
4) x^10
Step-by-step explanation:
1) If two numbers have the same base (i.e. x^3 and x^4) and you are multiplying them you just add the exponents. Therefore x^3*x^4 would be x^(3+4) which equals x^7.
2) When dividing similar bases you have to subtract the exponents. If we have x^18÷x^8 that is equivalent to x^(18-8) which gives us x^10.
3) If we have (x^3)^3 we will need to multiply the exponents. Therefore (x^3)^3 is equivalent to x^(3*3) which gives us x^9.
4) (x^2*x^4)^4÷x^8
First do what's in the parentheses,
(x^2*x^4) = x^6
Next do the exponents,
(x^6)^3 = x^18
Lastly the division,
x^18÷x^8 = x^10
x^10 is our answer.
