Use implicit differentiation to find \( \displaystyle \frac{dy}{dx} \).

1. \( \displaystyle 7x^3y^5-4x^7+5y^9=6y+13\)


Solution


2. \( \displaystyle \sin(x)\sin(y)=\sin{(xy)}\) .


Solution


3. Given \( \displaystyle x^5y^3+4x^3=2y^2-8 \).

(a) Find \( \displaystyle \frac{dy}{dx} \).

Solution


(b) Find the equation of the tangent line to the above curve at \( (0,2) \)

Solution



4. Find the derivative of the function.

(a)\(y=\sin^{-1}( 7x^5-2x^8)\)

Solution


(b) \( y=\tan^{-1}( \sqrt[3]{x}+\sqrt[5]{x}) \)

Solution