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To differentiate this, we must use the Chain Rule . This is because we have two functions multiplied by each other: (x) sin⁡(x). We use the substitution u = sin(x). This is our initial function, and we can s...

The first thing to remember is that the tangent to the curve at a given point has the same gradient as the curve at that point. Let's consider the general case y=f(x) at a point c=(x1,y1). Step 1:We have to ...

Firstly, note that cos^2(x)+5sin^2(x)= cos^2(x) +sin^2(x) +4sin^2(x). By trignoemtric identies, cos^2(x)+sin^2(x)=1 and so we can just integrate 1+4sin^2(x) since this is equal to cos^2(x)+5sin^2(x). Again, ...

Using the knowledge of a 2 = b 2 + c 2 - 2bcCos(A) Rearrange to aquire Cos(A) = (b 2 + c 2 - a 2 )/2bc Then input the values to obtain the angles of 42, 69, 69.

d/dx(4x 3 + 2x) = d/dx (4x 3 ) + d/dx(2x) = 4(3x 2 ) + x = 12x 2 + x