What is the d/(dt)(cos(t^2)) ?

The d/(dt)(cos(t^2)) is -sin(t^2)*2t

What is the first d/(dt)(cos(t^2)) ?

The first d/(dt)(cos(t^2)) is -sin(t^2)*2t

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

- sin (t^{2}) \cdot 2 t

Solution steps

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

Apply the chain rule:

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

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

\frac{d}{d t} (t^{2}) = 2 t

= - sin (t^{2}) \cdot 2 t

\frac{d}{d x} (\frac{π}{x})

\frac{d}{d x} (- 3 x^{4} - \frac{1}{x} + x x)

x \to - \frac{π}{4} lim (- sec (2 x))

f (x) = (3 x^{2} + 4 x - 19)^{15}

y^{^{'}} + y cos (x) = 5 cos (x)