Find the derivative of the function: $f\left(x\right)=cos\left(x^2\right)$. Which of the following is correct?

In Exercises 47 and 48, find an equation for

(b) the horizontal tangent line to the curve at Q.

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Theory and Examples

The equations in Exercises 49 and 50 give the position s = f(t) of a body moving on a coordinate line (s in meters, t in seconds). Find the body’s velocity, speed, acceleration, and jerk at time t = π/4 sec.

s = 2 − 2 sin t

Is there a value of b that will make

g(x) = { x + b, x < 0

cos x, x ≥ 0

continuous at x = 0? Differentiable at x = 0? Give reasons for your answers.

Differentiate the function: $f\left(x\right)=xcos\left(x\right)sin\left(x\right)$. Which of the following is the correct derivative $f^{\prime }\left(x\right)$?

Which of the following is the correct derivative of $csc\left(x\right)$ with respect to $x$?

Differentiate the function: $f\left(t\right)={ln\left(t\right)}^{2}cos\left(t\right)$. Which of the following is the correct derivative $f^{\prime }\left(t\right)$?

Find the derivative of the function.

$h\left(t\right)=\sin \left(t\right)\cos \left(t\right)$

Find the derivative of the function.

$f\left(x\right)=\frac{5\cos x}{2x^3}$