Find the derivative of \(y = \sin^{2} (5x)\) with respect to x.

The slope of the tangent to the curve y = 3x\(^2\) - 2x + 5 at the point (1, 6) is

Evaluate \(\int \sin 3x \mathrm d x\)

A circle with radius 5cm has its radius increasing at the rate of 0.2m/s. What will be the corresponding increase in the area?

If \(y = x^2 - \frac{1}{x}\). find dy/dx