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The derivative of sin (x²) w.r.t. x, at x = √π is :
Check whether the function f(x) = x² |x| is differentiable at x = 0 or not.
If y = √(tan √x), prove that √x (dy/dx) = (1 + y⁴)/(4y).
The traffic police has installed Over Speed Violation Detection (OSVD) system at various locations in a city. These cameras can capture a speeding vehicle from a distance of 300 m and even function in the dark. A camera is installed on a pole at the height of 5 m. It detects a car travelling away from the pole at the speed of 20 m/s. At any point, x m away from the base of the pole, the angle of elevation of the speed camera from the car C is θ. On the basis of the above information, answer the following questions :
The derivative of tan⁻¹(x²) w.r.t. x is :
If f(x) = |tan 2x|, then find the value of f′(x) at x = π/3.
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