Use the chain rule to find dz/dt calculator

We need to find:

z' (t) = dz (t) dt=ddt (e-3t· (-sin (2t)) 2) =

z' (t) = dz (t) dt=ddt (e-3t· (-sin? (2t)) 2) =

ddt (e-3tsin2 (2t)) = e-3tsin (2t) (4cos (2t) - 3sin (2t))

ddt (e-3tsin2? (2t)) = e-3tsin? (2t) (4cos? (2t) - 3sin? (2t))

Using:

The product rule:

ddt (f (t) ·y (t)) = f (t) ·ddt (y (t)) + y (t) ·ddt (f (t)) = y (t) ·f' (t) + f (t) ·y' (t) ddt (f (t) ·y (t)) = f (t) ·ddt (y (t)) + y (t) ·ddt (f (t)) = y (t) ·f' (t) + f (t) ·y' (t) ddt (ex (t)) = ex (t) ·ddt (x (t)) = x' (t) ·ex (t)

ddt (ex (t)) = ex (t) ·ddt (x (t)) = x' (t) ·ex (t)

When CC is a constant:

ddt (C·q (t)) = C·ddt (q (t)) = C·q' (t)

ddt (C·q (t)) = C·ddt (q (t)) = C·q' (t)

When nn is a constant, using the chain rule:

ddt (w (t) n) = n·w (t) n-1·ddt (w (t)) = n·w (t) n-1·w' (t)

ddt (w (t) n) = n·w (t) n-1·ddt (w (t)) = n·w (t) n-1·w' (t)

When mm is a constant, using the chain rule: ddt (v (mt)) = ddt (mt) ·v' (mt) = m·v' (mt)