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5 = a(3x+2) + b(x-1), x = 1, 5 = a(3+2) +b (1-1), 5 = a(5) + b(0), 5 = 5a, a = 1, x = -2/3, 5 = a(-2+2) + b(-(2/3)-1), 5 = a(0) + b(-5/3), 5 = -5b/3, b = -3, Therefore: 5/[(x-1)(3x+2)] = 1/(x-1) -3/(3...

You will have to use the Product Rule. The Product rule: when y=f(x)g(x), then dy/dx=f'(x)g(x)+f(x)g'(x). In this example, f(x)=sin(x) and g(x)=cos(x). Hence f'(x)=cos(x) and g'(x)=-sin(x). Using these an...

dy/dx = 2xcos(x²+2)

Using the chain rule, we know that dy/dx = dy/dt . dt/dx Therefore we differentiate both equations with respect to t:dx/dt = -4dy/dt = -2/(t^2)therefore dy/dx = -1/4 . -2/(t^2)dy/dx = 1/(2t^2) ... (we kno...

tan(x) is defined as sin(x)/cos(x) For a function which can be written as f(x) = u(x)/v(x) the quotient rule can be appliedThe quotient rule states f ' (x) = (u'v-v'u)/v^2 Applying this to the formula for...