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Differentiating a function, A straight line has a constant gradient, or in other words, the rate of change of y with respect to x is a constant. Example Consider the straight line y = 3x + 2 We can calculate the gradient of this line as follows. We take two points and calculate the change in y divided by the change in x. When x changes from −1 to 0, y changes from −1 to 2, and so No matter which pair of points we choose the value of the gradient is always 3. y is a function of x, so y =f(x) f(x1) = y1 and f(x2) =y2 x2-x1=dx, x2= x1+dx, By substitituting these terms in slope formula, we have; m =[ f(x1 + dx) - f(x1)]/dx, as the limit of dx approaches 0 Seven steps to avoit the spread of Corona Virus (Covid19): If you find this video interesting, kindly subscribe to my channel for more exciting Maths tutorials. Subscribe link: #Differentiation #First #Principles WhatsApp group: Facebook: Instagram: Linkedin: Blog:

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To solve any Second Order Linear Homogeneous Differential Equation, first this you need to do, is to transform the equation in to an auxiliary or characteristics equation in the form: ar²+be+c=0 We have already seen how to do that in our previous lesson. The next move is to solve for r which are the roots of the equation (r intercept). Then determine the nature of the roots and substitute in to the following equations, depending on the nature of roots. y=C₁eʳ¹ˣ+C₂eʳ²ˣ. when you obtain real and distinct roots y=(C₁+C₂x)eʳˣ when you Obtain real and equal roots. and finally, if you Obtain a complex solution in the form: r= m+si or r = m-si where i is imaginary number, and m and s are real numbers, then y=eᵐˣ[C₁cos(st)+C₂sin(st)]

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Happy Ney Year 2021 Mathematics #2021 #HappyNewYear #Mathematics