Solving: $\frac{d}{dx}\left(e^{xy}-4xy^3=3x^2\right)$
Exercise
$\frac{dy}{dx}\left(e^{xy}-4xy^3=3x^2\right)$
Step-by-step Solution
Learn how to solve problems step by step online. Find the implicit derivative d/dx(e^(xy)-4xy^3=3x^2). 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. The power rule for differentiation states that if n is a real number and f(x) = x^n, then f'(x) = nx^{n-1}. Multiply 3 times 2.
Find the implicit derivative d/dx(e^(xy)-4xy^3=3x^2)
Final answer to the exercise
$y^{\prime}=\frac{6x-ye^{xy}+4y^3+12xy^{\left(2+{\prime}\right)}}{e^{xy}x}$