Page:Calculus Made Easy.pdf/274



(1) $$\dfrac{dy}{dx} = 13x^{12}$$.

(2) $$\dfrac{dy}{dx} = - \dfrac{3}{2} x^{-\frac{5}{2}}$$.

(3) $$\dfrac{dy}{dx} = 2ax^{(2a-1)}$$.

(4) $$\dfrac{du}{dt} = 2.4t^{1.4}$$.

(5) $$\dfrac{dz}{du} = \dfrac{1}{3} u^{-\frac{2}{3}}$$.

(6) $$\dfrac{dy}{dx} = -\dfrac{5}{3}x^{-\frac{8}{3}}$$.

(7) $$\dfrac{du}{dx} = -\dfrac{8}{5}x^{-\frac{13}{5}}$$.

(8) $$\dfrac{dy}{dx} = 2ax^{a-1}$$.

(9) $$\dfrac{dy}{dx} = \dfrac{3}{q} x^{\frac{3-q}{q}}$$.

(10) $$\dfrac{dy}{dx} = -\dfrac{m}{n} x^{-\frac{m+n}{n}}$$.

(1) $$\dfrac{dy}{dx} = 3ax^2$$.

(2) $$\dfrac{dy}{dx} = 13 \times \frac{3}{2}x^{\frac{1}{2}}$$.

(3) $$\dfrac{dy}{dx} = 6x^{-\frac{1}{2}}$$.

(4) $$\dfrac{dy}{dx} = \dfrac{1}{2}c^{\frac{1}{2}} x^{-\frac{1}{2}}$$.

(5) $$\dfrac{du}{dz} = \dfrac{an}{c} z^{n-1}$$.

(6) $$\dfrac{dy}{dt} = 2.36t$$.

(7) $$\dfrac{dl_t}{dt} = 0.000012\times l_0$$.

(8) $$\dfrac{dC}{dV} = abV^{b-1}$$, $$0.98$$, $$3.00$$ and $$7.47$$ candle power per volt respectively.

(9) $$\dfrac{dn}{dD} = -\dfrac{1}{LD^2} \sqrt{\dfrac{gT}{\pi \sigma}}, \dfrac{dn}{dL} = -\dfrac{1}{DL^2} \sqrt{\dfrac{gT}{\pi \sigma}}$$. $$\;\quad \dfrac{dn}{d \sigma} = -\dfrac{1}{2DL} \sqrt{\dfrac{gT}{\pi \sigma^3}}, \dfrac{dn}{dT} = \dfrac{1}{2DL} \sqrt{\dfrac{g}{\pi \sigma T}}$$.