Implicit Differentiation

Implicit Differentiation - Exponential and Logarithmic Functions


If y10+x5y6=2+yex2,\displaystyle y^{10}+x^{5}y^{6}=2+ye^{x^2}, what is dydx?\displaystyle \frac{dy}{dx}?

If exy=4x6y,\displaystyle e^{\frac{x}{y}}=4x-6y, what is dydx?\displaystyle \frac{dy}{dx}?

What is the equation of the tangent line to ln(x+4y)+3ey=3\ln (x+4y)+3e^y=3 at the point (1,0)?(1,0)?

If y=(lnx)xy=(\ln x)^x, what is the derivative of yy at x=ex=e?

Given e2xy=y2e^{2xy} = y^2, what is the value of dydx\frac{dy}{dx} at (x,y)=(0,1)(x,y) = (0,1) .


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