Solving: $\frac{d}{dx}\left(\tan\left(x-4y\right)=3x+y^2\right)$
Exercise
$\frac{dy}{dx}\left(tan\left(x-4y\right)=3x+y^2\right)$
Step-by-step Solution
Learn how to solve problems step by step online. Find the implicit derivative d/dx(tan(x-4y)=3x+y^2). Apply implicit differentiation by taking the derivative of both sides of the equation with respect to the differentiation variable. The derivative of the tangent of a function is equal to secant squared of that function times the derivative of that function, in other words, if {f(x) = tan(x)}, then {f'(x) = sec^2(x)\cdot D_x(x)}. The derivative of a sum of two or more functions is the sum of the derivatives of each function. The derivative of a sum of two or more functions is the sum of the derivatives of each function.
Find the implicit derivative d/dx(tan(x-4y)=3x+y^2)
Final answer to the exercise
$y^{\prime}=\frac{3-\sec\left(x-4y\right)^2}{-4\sec\left(x-4y\right)^2-2y}$