Solving: $\frac{d}{dx}\left(x^2=\left(4x^2y^3+1\right)^2\right)$
Exercise
$\frac{dy}{dx}\left(x^2=\left(4x^2y^3+1\right)^2\right)$
Step-by-step Solution
Learn how to solve polynomial factorization problems step by step online. Find the implicit derivative d/dx(x^2=(4x^2y^3+1)^2). Apply implicit differentiation by taking the derivative of both sides of the equation with respect to the differentiation variable. The power rule for differentiation states that if n is a real number and f(x) = x^n, then f'(x) = nx^{n-1}. Any expression to the power of 1 is equal to that same expression. The power rule for differentiation states that if n is a real number and f(x) = x^n, then f'(x) = nx^{n-1}.
Find the implicit derivative d/dx(x^2=(4x^2y^3+1)^2)
Final answer to the exercise
$x=0,\:1-32y^{6}x^2-48x^{3}y^{\left({\prime}+5\right)}-8y^{3}-12xy^{\left({\prime}+2\right)}=0$