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First note that a=e ln(a) and ln(a b )=b ln(a)By substituting a=3 x we get a=3 x =e ln(3^x) =e x ln(3) , and hence f(x)=e x ln(3) +2∫ f(x)dx=∫ e x ln(3) +2 dx . First we can split this into the sum of two in...

Put the equation in the form Rsin(x-a) (=Rsin(x)cos(a)-Rcos(x)sin(a)). Looking at the original equation Rcos(a) = 2 and Rsin(a) = 1.5. Tan(a)=1.5/2 and R^2= 2^2 +1.5^2. Therefore R = 2.5 and a = 0.6435.The m...

Write out the product rule: if y=f(x)g(x) where f and g are functions, dy/dx = f'(x)g(x) + f(x)g'(x) Substitute in the expressions from the question:Therefore if f(x)=cos(3x) and g(x) = cosec(5x), f'(x) = -3...

start of by expanding the braquet which has got a power(x + 2y) (x + 2y) = X 2 + 2xy + 2xy + 4Y 2 then simplify that => x 2 + 4xy + 4y 2 then multiply that by (x - 6) (x - 6) (x 2 + 4xy + 4y 2 ) = x 3 + 4...

First thing you would do is write down the coordinates where the tangent meets the curve. After that you would differenciate the equation (f(x)) of the curve (do dy/dx) in order to get f'(x).Then you would s...