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You must apply the chain rule whenever you see a function contained within another function. For example, if you were to differentiate (sin x)²  you would apply the chain rule as the sin functi...

This problem will be solved using the integration by parts method, taking the integrated function as udv which answer is uv-(integration of vdu) : u=x and dv=cos(x) so, du=dx and v=sin(x). We have, xsin(x...

the derivative of sinx is cosx, then we know that we can apply the product rule to find derivative of xsinx, such that if we let u=x and v=sinx and apply the formula d/dx(xsinx)=udv/dx+vdu/dx. to...

Firstly remember that each part of the equation can be differentiated separately. Let's label each part:

Part A: 2(x^2)y

Part B: 2x

Part C: 4y

Part D: -cos(piy)

Part E: ...

There will be intersection when x^2 + 4x + 3 = kx + 2. Our goal is to find the values of k which would only give one solution to this quadratic equation, which would make the lines 'tangent' to each other...