Question

Implicit differentiation help!

Answer 1

Use Implicit differentiation to find an equation for the tangent line to the curve
\[x^3-3xsqrt(2y+1)+y^2+2=0 \]

Answer 2

like this ?
\[ x^3-3x\sqrt{2y+1}+y^2+2=0 \]

Answer 3

or using a power of 1/2
\[ x^3-3x(2y+1)^{\frac{1}{2}}+y^2+2=0 \]

take the derivative with respect to x, and treat both x and y as variables.

Answer 4

\[ 3x^2 + -3x\ d(2y+1)^{\frac{1}{2}} + -3 (2y+1)^{\frac{1}{2}} + 2y\ y' \]
\[ 3x^2 + -3x\ \frac{1}{2}(2y+1)^{-\frac{1}{2}} \cdot 2\ y'+ -3 (2y+1)^{\frac{1}{2}} + 2y\ y' \]
now you have to simplify that and solve for y'