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Popular >

d/(dt)(2tsin(t)-(t^2-2)cos(t))

Solution

\frac{d}{d t} (2 t sin (t) - (t^{2} - 2) cos (t))

Solution

t^{2} sin (t)

Solution steps

\frac{d}{d t} (2 t sin (t) - (t^{2} - 2) cos (t))

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{d}{d t} (2 t sin (t)) - \frac{d}{d t} ((t^{2} - 2) cos (t))

\frac{d}{d t} (2 t sin (t)) = 2 (sin (t) + t cos (t))

\frac{d}{d t} ((t^{2} - 2) cos (t)) = 2 t cos (t) - sin (t) (t^{2} - 2)

= 2 (sin (t) + t cos (t)) - (2 t cos (t) - sin (t) (t^{2} - 2))

Simplify

2 (sin (t) + t cos (t)) - (2 t cos (t) - sin (t) (t^{2} - 2)) : t^{2} sin (t)

= t^{2} sin (t)

Graph

Popular Examples

(dy)/(dx)-y/x =x^2y^2

\frac{d y}{d x} - \frac{y}{x} = x^{2} y^{2}

derivative of x^3+y^3-3xy

\frac{d}{d x} (x^{3} + y^{3} - 3 x y)

limit as x approaches-1+of 2x^2-4x+2

x \to - 1 + lim (2 x^{2} - 4 x + 2)

limit as x approaches 1 of sqrt(x-1)

x \to 1 lim (x - 1)

integral of x^4(5x^5+9)^7

\int x^{4} (5 x^{5} + 9)^{7} d x

Frequently Asked Questions (FAQ)

What is the d/(dt)(2tsin(t)-(t^2-2)cos(t)) ?
The d/(dt)(2tsin(t)-(t^2-2)cos(t)) is t^2sin(t)
What is the first d/(dt)(2tsin(t)-(t^2-2)cos(t)) ?
The first d/(dt)(2tsin(t)-(t^2-2)cos(t)) is t^2sin(t)