What is the derivative of sin(arccos(t)) ?

The derivative of sin(arccos(t)) is -t/(sqrt(1-t^2))

What is the first derivative of sin(arccos(t)) ?

The first derivative of sin(arccos(t)) is -t/(sqrt(1-t^2))

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derivative of

sin (arccos (t))

- \frac{t}{1 - t ^{2}}

Solution steps

\frac{d}{d t} (sin (arccos (t)))

Simplify

sin (arccos (t)) : 1 - t^{2}

= \frac{d}{d t} (1 - t^{2})

Apply the chain rule:

\frac{1}{2 1 - t ^{2}} \frac{d}{d t} (1 - t^{2})

= \frac{1}{2 1 - t ^{2}} \frac{d}{d t} (1 - t^{2})

\frac{d}{d t} (1 - t^{2}) = - 2 t

= \frac{1}{2 1 - t ^{2}} (- 2 t)

Simplify

\frac{1}{2 1 - t ^{2}} (- 2 t) : - \frac{t}{1 - t ^{2}}

= - \frac{t}{1 - t ^{2}}

\int \frac{1}{1 - 49 x ^{2}} d x

\int \frac{2}{x - 3} d x

\int \frac{x}{x + 4} d x

\frac{d}{d x} ((x^{2} - 3) (x^{3} - 2 x))

f (x) = \frac{2 x}{x ^{2} - 7}, (3, 3)

What is the derivative of sin(arccos(t)) ?
The derivative of sin(arccos(t)) is -t/(sqrt(1-t^2))
What is the first derivative of sin(arccos(t)) ?
The first derivative of sin(arccos(t)) is -t/(sqrt(1-t^2))