Calculus homework?

Question

1) find dy/dx of the implicit relation x^7 + y^7 - 7 axy = 0

2) Find the slope of the tangent to the curve x^2 + y^2 = 27 at x0 = 2

3) Find the value of the derivative of 2(x-y)^2 = xy at (2,1)

4) Find the second derivative of the function.
y = 3x^4 - x^3 + 3x

5) Find the second derivative of the function
y = 12 + x/ 12 - x

Answer 1

1) The equation

2) The curve

The derivative of the function is it's tangent slope.

The curve and tangent passe through x = 2

Slope of tangent line to the curve at

3) The equation

Derivative at the point (2,1)

Answer 2

4) The function

Apply derivative on each side with respect of x .

Apply the formula

Second derivative is

5) The function

Apply derivative on each side with respect of x.

Apply quotient rule in derivatives.

Again derivative on each side with respect of x.

Second derivative is