What is the d/(dt)(cot^3(pi-t)) ?

The d/(dt)(cot^3(pi-t)) is 3csc^4(t)cos^2(t)

What is the first d/(dt)(cot^3(pi-t)) ?

The first d/(dt)(cot^3(pi-t)) is 3csc^4(t)cos^2(t)

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\frac{d}{d t} (cot^{3} (π - t))

3 csc^{4} (t) cos^{2} (t)

Solution steps

\frac{d}{d t} (cot^{3} (π - t))

Simplify

cot^{3} (π - t) : - \frac{cos ^{3} ( t )}{sin ^{3} ( t )}

= \frac{d}{d t} (- \frac{cos ^{3} ( t )}{sin ^{3} ( t )})

Take the constant out:

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

= - \frac{d}{d t} (\frac{cos ^{3} ( t )}{sin ^{3} ( t )})

Apply the Quotient Rule:

(\frac{f}{g})^{'} = \frac{f ^{'} \cdot g - g ^{'} \cdot f}{g ^{2}}

= - \frac{\frac{d}{d t} ( cos ^{3} ( t ) ) sin ^{3} ( t ) - \frac{d}{d t} ( sin ^{3} ( t ) ) cos ^{3} ( t )}{( sin ^{3} ( t ) ) ^{2}}

\frac{d}{d t} (cos^{3} (t)) = - 3 cos^{2} (t) sin (t)

\frac{d}{d t} (sin^{3} (t)) = 3 sin^{2} (t) cos (t)

= - \frac{( - 3 cos ^{2} ( t ) sin ( t ) ) sin ^{3} ( t ) - 3 sin ^{2} ( t ) cos ( t ) cos ^{3} ( t )}{( sin ^{3} ( t ) ) ^{2}}

Simplify

- \frac{( - 3 cos ^{2} ( t ) sin ( t ) ) sin ^{3} ( t ) - 3 sin ^{2} ( t ) cos ( t ) cos ^{3} ( t )}{( sin ^{3} ( t ) ) ^{2}} : 3 csc^{4} (t) cos^{2} (t)

= 3 csc^{4} (t) cos^{2} (t)

\int 2 x e^{x} d x

\frac{d}{d x} (ln (cos^{4} (x)))

\int (5 y^{4}) d y

\int (2 x - 1) y^{2} sin (4 x y) d x

f (x) = 8 x - 3

What is the d/(dt)(cot^3(pi-t)) ?
The d/(dt)(cot^3(pi-t)) is 3csc^4(t)cos^2(t)
What is the first d/(dt)(cot^3(pi-t)) ?
The first d/(dt)(cot^3(pi-t)) is 3csc^4(t)cos^2(t)