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By product rule:u = 4sin(x) v = cos(3x)du/dx = 4cos(x) dv/dx = -3sin(3x)dy/dx = u (dv/dx) + v (du/dx)dy/dx = 4sin(x) * -3sin(3x) + cos(3x) * 4cos(x)dy/dx = -12sin(x)sin(3x) + 4cos(x)cos(3x)Evaluate at x = pi...

We can explain this by taking a simple power equation such as 2 3 = 8 and setting each number as an unknown variable. For instance 2 3 = x is solved by cubing 2, x 3 = 8 is solved by taking the cube root of ...

you cannot integrate cos^2(4x) without making substitutions first. Use the cos^2(x) + sin^2(x) = 1 identity with the cos(2x)=cos^2(x)-sin^2(x), rearrange to get the identity cos(2x) = 2cos^2(x) - 1, then cos...

Using simple trig identities, we know tan^2(A) + 1 = sec^2(A).Substituting for sec^2(A) into our equation, we get: tan^2(A) + 1 = 3 - tan(A).Moving this over to one side, we get the quadratic in terms of tan...

Although the unseen poetry section of an exam can seem intimidating, in my experience I've found it useful to begin by annotating the poem, and then using these annotations to structure your commentary. Ther...