Exercise
$\frac{d}{dx}\left(5x^3y^4+\frac{3y^2}{4x^3}=5xy\right)$
Step-by-step Solution
Learn how to solve problems step by step online. Find the implicit derivative d/dx(5x^3y^4+(3y^2)/(4x^3)=5xy). Apply implicit differentiation by taking the derivative of both sides of the equation with respect to the differentiation variable. The derivative of a function multiplied by a constant is equal to the constant times the derivative of the function. Apply the product rule for differentiation: (f\cdot g)'=f'\cdot g+f\cdot g', where f=x and g=y. The derivative of the linear function is equal to 1.
Find the implicit derivative d/dx(5x^3y^4+(3y^2)/(4x^3)=5xy)
Final answer to the exercise
$5\left(3x^{2}y^4+4x^3y^{3}y^{\prime}\right)+\frac{24y\cdot y^{\prime}x^3-36y^2x^{2}}{16x^{6}}=5\left(y+xy^{\prime}\right)$