Could you help me with my calc work?

Part 1 of 3 We want to find - by using implicit differentitation if x6 + y9 = 22 . For implicit differentiation problems, the assumption is that y is a function of x even if we can't write it as such. We start by taking the derivative of both sides of the equation with respect to x . x (* 6 + 19 ) = (22) Since the derivative is linear, - (x6 + y9) = (x6) + (x9). Now, (x5) = Part 2 of 3 (x6) = 6x5 . Similarly, the derivative of -(y") would be 9y, except since y is a function of x, we have to take the chain rule into account and so (9) = 98dy . dx Now, we can't forget to take the derivative of the right hand side of the equation as well. So. (22) = (No Response) 0 Part 3 of 3 dx Since the derivative of the left hand side of the original equation is 6x3 + 9/80% and the derivative of the right hand side is 0 , we can now solve the new equation for dx Thus, dy = dx XIf A(x) + x2[A(x)]= = 10 and f(1) = 2, find f '(1). f '(1) = XUse implicit differentiation to find an equation of the tangent line to the curve at the given point. 6(x2 + 2)2 = 169(x2 - y2) (5 , 1 ) (lemniscate) E XUse implicit differentiation to find an equation of the tangent line to the curve at the given point. x3ty = 7xy (-4, 2) (Folium of Descartes) X\fFind y" by implicit differentiation. 3x3 + 5/3 = 3 X