The dervatives of hyperbolic functions are as under: So, now you will be quite aware of the differentiation formulas, i.e. Here, \(\frac{dy}{dx} \) represents the rate of change of y with respect to x. f0(x) (3) d dx [f(x)g(x)] = f(x)g0(x)+g(x)f0(x) (4) d dx f(x) g(x) = g(x)f0(x)−f(x)g0(x) [g(x)]2. You can solve differential calculus questions for free on Embibe. For problems 1 – 12 find the derivative of the given function. \(\frac{d}{dx}(\tanh^{-1} ~ x)\) = \(\frac{1}{{1-x^2}}\), j. In all the formulas below, f’ means \( \frac{d(f(x))}{dx} = f'(x)\) and g’ means \(\frac{d(g(x))}{dx}\) = \(g'(x)\) . Download the BYJU’S app to get interesting and personalised videos and have fun learning. Please note that if you are getting difficulty in accessing these differential formulas on your mobile devices. Sine (sin), cosine (cos), tangent (tan), secant (sec), cosecant (cosec), and cotangent (cot) are the six commonly used trigonometric functions each of which represents the ratio of two sides of a triagnle. h�b```f``2a`2�02 � P90A6�7�o�|��@�gkS�XcXC�� �\�;V�^�Q R+6=�Hlzp�%���T�I������5��,�����a�N���f��T�S-&��OL������4���M��s ��� This is a function that we can differentiate. Ans: You can practice free differential calculus questions at Embibe. \(\frac{d}{dx}(\sin^{-1}~ x)\) = \(\frac{1}{\sqrt{1-x^2}}\), b. The deivatives of inverse trigonometric functions are as under: The hyperbolic function of an angle is expressed as a relationship between the distances from a point on a hyperbola to the origin and to the coordinate axes. 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