Implicit Derivative Calculus

 $\left(x^3+2y^2\right)^5=y$  find dy/dx in terms of x and y.

•  $\frac{-15x^2\left(x^3+2y^2\right)^4}{20y\left(x^3+2y^2\right)^4-1}$  

•  $-\frac{3x^2}{4y}$  

•  $-\frac{30x^2\left(x^3+2y^2\right)^4}{15y\left(x3+2y^2\right)^6-1}$  

•  $-\frac{6x^2}{8y}$  

 $\sin\left(x^3y^3\right)=3x,\$  find dy/dx

•  $\frac{1-y^3x^6\cos\left(x^3y^3\right)}{3x^3y^2\cos\left(x^3y^3\right)}$  

•  $\frac{3-3x^2y^3\cos\left(x^3y^3\right)}{3x^3y^2\cos\left(x^3y^3\right)}$  

•  $3-3x^2y^3\cos\left(x^3y^3\right)$  

 $\cos\left(xy^2\right)=x$  find dy/dx

•  $\frac{1+y^2\sin\left(xy^2\right)}{-2xy\sin\left(xy^2\right)}$  

•  $\frac{1\sin\left(xy^2\right)}{-2xy\sin}$   $\$  

•  $2xyy\sin\left(xy^2\right)$  

 $\sqrt{x+2y}=5y$  find dy/dx

•  $\frac{\frac{1}{2}\left(x+4y\right)^{\frac{1}{2}}}{\left(x+2y\right)^{\frac{1}{2}}+10}$  

•  $-\frac{\frac{1}{2}\left(y+2x\right)^{-\frac{1}{2}}}{\left(y+2x\right)^{-\frac{1}{2}}-10}$   $\$  

•  $\frac{-\frac{1}{2}\left(x+2y\right)^{-\frac{1}{2}}}{\left(x+2y\right)^{-\frac{1}{2}}-5}$  

 $\sin\left(x+y^3\right)=5y^3$  find dy/dx

•  $\frac{-\cos\left(x+y^3\right)}{6y^2\cos\left(x+y^3\right)-25y^2}$  

•  $\frac{-\cos\left(x+y^3\right)}{3y^2\cos\left(x+y^3\right)-15y^2}$   $\$  

•  $\frac{-\sin\left(x+y^3\right)}{3y^2\sin\left(x+y^3\right)-15y^2}$  

 $\cos\left(2x+3y^3\right)=3y^2$  find dy/dx

•  $\frac{4\sin\left(2x+2y^3\right)}{-21y^2\sin\left(6x+3y^3\right)-1y}$  

•  $\frac{2\sin\left(2x+3y^3\right)}{-9y^2\sin\left(2x+3y^3\right)-6y}$   $\$  

•  $\frac{12\sin\left(12x+33y^3\right)}{-19y^2\sin\left(12x+33y^3\right)-6y}$  

 $\cos\left(x+5y^2\right)=x^3$  find dy/dx

•  $\frac{3x^2+\sin\left(x+5y^2\right)}{-5y\sin\left(x+10y^2\right)}$  

•  $\frac{3x^2+\sin\left(x+5y^2\right)}{-10y\sin\left(x+5y^2\right)}$   $\$  

•  $\frac{3x^3+\sin\left(x+5y^3\right)}{-10y\sin\left(x+5y^3\right)}$  

 $\left(2x^3+5y\right)^6=3y$  find dy/dx

•  $\frac{-36x^2\left(2x^3+5y\right)^5}{30\left(2x^3+5y\right)^5-3}$  

•  $\frac{36x^2\left(4x^3+5y\right)^{10}}{15\left(4x^3+5y\right)^{10}-3}$   $\$  

•  $\frac{-3x^2\left(23x^3+1y\right)^5}{10\left(23x^3+1y\right)^5-3}$  

 $\cos\left(x+4y\right)=y$  find dy/dx

•  $\frac{\sin\left(x+4y^2\right)}{-4\sin\left(x+4y^2\right)}$  

•  $\frac{\cos\left(x+1y\right)}{-1\cos\left(x+1y\right)-1}$   $\$  

•  $\frac{\sin\left(x+4y\right)}{-4\sin\left(x+4y\right)-1}$  

 $\sin\left(5xy\right)=y^2$  find dy/dx

•  $\frac{-5y\cos\left(5xy\right)}{5x\cos\left(5xy\right)-2y}$  

•  $\frac{10y\cos\left(5xy\right)}{10x\cos\left(5xy\right)+4y}$   $\$  

•  $\frac{-15y\cos\left(-5xy\right)}{15x\cos\left(-5xy\right)-2y}$