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Popular >

d/(dt)(((sqrt(2)ty))/3)

Solution

\frac{d}{d t} (\frac{( 2 t y )}{3})

Solution

\frac{2}{3} (y + t \frac{d y}{d t})

Solution steps

\frac{d}{d t} (\frac{( 2 t y )}{3})

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

= \frac{2}{3} \frac{d}{d t} (t y)

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = t, g = y

= \frac{2}{3} (\frac{d t}{d t} y + \frac{d y}{d t} t)

\frac{d t}{d t} = 1

= \frac{2}{3} (1 \cdot y + \frac{d y}{d t} t)

Simplify

= \frac{2}{3} (y + t \frac{d y}{d t})

Popular Examples

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y = e^{x}, y = 2 e^{- x} + 1, x = 0

(\partial)/(\partial x)(-4sin(2x))

\frac{\partial}{\partial x} (- 4 sin (2 x))

implicit (dy)/(dx),x^3+y^3=36 implicit derivative

\frac{d y}{d x}, x^{3} + y^{3} = 36

slope of (0,1),(1,-3)slope

(0, 1), (1, - 3)

limit as x approaches-infinity of x-4

x \to - \infty lim (x - 4)

Frequently Asked Questions (FAQ)

What is the d/(dt)(((sqrt(2)ty))/3) ?
The d/(dt)(((sqrt(2)ty))/3) is (sqrt(2))/3 (y+t(dy)/(dt))
What is the first d/(dt)(((sqrt(2)ty))/3) ?
The first d/(dt)(((sqrt(2)ty))/3) is (sqrt(2))/3 (y+t(dy)/(dt))