Page:Calculus Made Easy.pdf/194

 (4) If $$y = \sin a^x$$, find $$\dfrac{dy}{dx}$$.

(5) Differentiate $$y=\log_\epsilon \cos x$$.

(6) Differentiate $$y=18.2 \sin(x+26^\circ)$$.

(7) Plot the curve $$y=100\sin(\theta-15^\circ)$$; and show that the slope of the curve at $$\theta = 75^\circ$$ is half the maximum slope.

(8) If $$y=\sin \theta\cdot\sin 2\theta$$, find $$\dfrac{dy}{d\theta}$$.

(9) If $$y=a\cdot\tan^m(\theta^n)$$, find the differential coefficient of $$y$$ with respect to $$\theta$$.

(10) Differentiate $$y=\epsilon^x \sin^2 x$$.

(11) Differentiate the three equations of Exercises XIII. (p. 163), No. 4, and compare their differential coefficients, as to whether they are equal, or nearly equal, for very small values of $$x$$, or for very large values of $$x$$, or for values of $$x$$ in the neighbourhood of $$x=30$$.

(12) Differentiate the following:

(13) Differentiate $$y=\sin(2\theta +3)^{2.3}$$.

(14) Differentiate $$y=\theta^3+3 \sin(\theta+3)-3^{\sin \theta} - 3^\theta$$.

(15) Find the maximum or minimum of $$y=\theta \cos \theta$$