What is derivative of x=cos^4(t) ?

The answer to derivative of x=cos^4(t) is (dt)/(dx)=-1/(4cos^3(t)sin(t))

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derivative of x=cos^4(t)

derivative of

x = cos^{4} (t)

\frac{d t}{d x} = - \frac{1}{4 cos ^{3} ( t ) sin ( t )}

Solution steps

x = cos^{4} (t)

Treat

t

t (x)

Differentiate both sides:

1 = - 4 cos^{3} (t) sin (t) \frac{d t}{d x}

Isolate

\frac{d t}{d x} : \frac{d t}{d x} = - \frac{1}{4 cos ^{3} ( t ) sin ( t )}

\frac{d t}{d x} = - \frac{1}{4 cos ^{3} ( t ) sin ( t )}

x^{4} + y^{4} = 4 a^{2} x^{3} y^{3}

(d^{2} + d) \cdot y = x^{2} + 2 x + 4

(d^{2} + d) y = x^{2} + 2 x + 4

x = e^{s i n (t^{2} - 4 t)}

(d^{2} + 1) \cdot y = x^{2} \cdot (cos (x))

What is derivative of x=cos^4(t) ?
The answer to derivative of x=cos^4(t) is (dt)/(dx)=-1/(4cos^3(t)sin(t))