Provide an appropriate response.Find dy/dx by implicit differentiation. x3 + y3 = 5

Provide an appropriate response.Find for .

Differentiate.Find f'(t) for f(x) = (3x – 3)(5×3 – x2 + 1)

Differentiate.Find f'(t) for f(x) = (5x – 5)(3×3 – x2 + 1)

Provide an appropriate response.Let C(x) be the cost function and R(x) the revenue function. Compute the marginal cost, marginal revenue, and the marginal profit functions.C(x) = 0.0004×3 – 0.048×2 + 300x + 20,000R(x) = 400x

Provide an appropriate response.Let C(x) be the cost function and R(x) the revenue function. Compute the marginal cost, marginal revenue, and the marginal profit functions.C(x) = 0.0005×3 – 0.012×2 + 100x + 30,000R(x) = 450x

Differentiate.Find f'(t) for f(x) =

Find the equation of the tangent line to the curve when x has the given value.f(x) = 4- x2; x = 8

Solve the problem.How long will it take for the value of an account to be $890 if $350 is deposited at 11% interest compounded continuously? Round your answer to the nearest hundredth.

Provide an appropriate response.Let C(x) be the cost function and R(x) the revenue function. Compute the marginal cost, marginal revenue, and the marginal profit functions.C(x) = 0.0003×3 – 0.024×2 + 300x + 10,000R(x) = 400x