## Step-by-step explanation

Problem to solve:

Learn how to solve limits problems step by step online.

$\lim_{x\to0}\left(\frac{\frac{d}{dx}\left(\sin\left(3x\right)\right)}{\frac{d}{dx}\left(\tan\left(4x\right)\right)}\right)$

Learn how to solve limits problems step by step online. Evaluate the limit of (sin(3*x)/(tan(4*x) as x approaches 0. If we try to evaluate the limit directly, it results in indeterminate form. Then we need to apply L'Hôpital's rule. The derivative of the sine of a function is equal to the cosine of that function times the derivative of that function, in other words, if {f(x) = \sin(x)}, then {f'(x) = \cos(x)\cdot D_x(x)}. The derivative of the linear function times a constant, is equal to the constant. 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)}.