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To find the maximum/minimum of a curve you must first differentiate the function and then equate it to zero. This gives you one coordinate. To find the other you must resubstitute the one already found in...

To differentiate y=(x²+4x)⁵ you need to use the chain rule. The chain rule uses the fact that dy/dx = dy/dt * dt/dx. 

Here we create a new variable t, where t = x²+...

3(3/4)x^(-1/4) which simplifies to (9/4)x^(-1/4)

Note: for what’s about to come, ' denotes derivative with respect to x. Method 1 (integration by parts): let I = (e^x)sin(x) dx let u = sin(x)...