Could you help me with my calc work?

If f(x) + x [f(x)]3 = 10 and f(1) = 2, find f '(1). f '(1) =Use implicit differentiation to find an equation of the tangent line to the curve at the given point. x' + xy + y= = 3, (1, 1) (ellipse) V =Use implicit differentiation to find an equation of the tangent line to the curve at the given point. x2 + 2xy - y~ + x = 5, (3, 7) (hyperbola)Use implicit differentiation to find an equation of the tangent line tn the curve at the given point. 4E)? + 112} = [x2 + y: 1:612 to. 2) IIIJ'rnacenj We want to find - by using implicit differentitation if x6 + 19 = 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 . d ( * 6 + ys ) = (22 ). Since the derivative is linear, (x6 + 1s) =. dx * 6 ) + (19 ) Now, 0 ( x 5 )