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calumus meretrix et gladio innocentis

### Calculus Rule Exercises Answers

Exercises from public domain textbooks. Solutions where provided do not necessary follow the same lines as the original.

A55-1. {$$\frac{dy}{dx}= 6x$$} worked

A55-2. {$$\frac{dy}{dx}= 2x$$}

A55-3. {$$\frac{dy}{dx}= -4$$}

A55-4. {$$\frac{ds}{dt}= 4t$$}

A55-5. {$$\frac{dy}{dx}= -\frac{1}{x^2}$$}

A55-6. {$$\frac{dy}{dx}= -\frac{-2}{x^2}$$}

A55-7. {$$\frac{dy}{dx}= 3x^2$$}

A55-8. {$$\frac{dy}{dx}= 4x$$}

A55-9. {$$\frac{dy}{dx}= 4x$$}

A55-10. {$$\frac{d\rho}{d\theta}= 2a\theta$$}

A55-11. {$$\frac{dy}{dx}= -\frac{4}{x^3}$$}

A55-12. {$$\frac{dy}{dx}= -\frac{3}{(x - 1)^2}$$}

A55-28. {$$y^{\prime} = 2x - 3$$}

A55-29. {$$s^{\prime} = 4t + 5$$}

A55-30. {$$\rho^{\prime} = 15\theta^2 - 2$$}

A55-31. {$$y^{\prime} = 2ax + b$$}

B24-1. {$$\dfrac{dy}{dx} = 13x^{12}$$}

B24-2. {$$\dfrac{dy}{dx} = - \dfrac{3}{2} x^{-\frac{5}{2}}$$}

B24-3. {$$\dfrac{dy}{dx} = 2ax^(2a-1)$$}

B24-4. {$$\dfrac{du}{dt} = 2.4t^{1.4}$$}

B24-5. {$$\dfrac{dz}{du} = \dfrac{1}{3} u^{-\frac{2}{3}}$$}

B24-6. {$$\dfrac{dy}{dx} = -\dfrac{5}{3}x^{-\frac{8}{3}}$$}

B24-7. {$$\dfrac{du}{dx} = -\dfrac{8}{5}x^{-\frac{13}{5}}$$}

B24-8. {$$\dfrac{dy}{dx} = 2ax^{a-1}$$}

B24-9. {$$\dfrac{dy}{dx} = \dfrac{3}{q} x^{\frac{3-q}{q}}$$}

B24-10. {$$\dfrac{dy}{dx} = -\dfrac{m}{n} x^{-\frac{m+n}{n}}$$}

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### December 23, 2018

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