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Integration by parts is used to integrate a product of functions. The formula is as follows:
Int[f(x)g'(x)] = f(x)g(x) - Int [f'(x)g(x)]
You must first identify the names of the two sides in relation to the angle you are trying to find out. The technique "sohcahtoa" is generally very helpful in working this out. This abbreviat...
Step 1: Rearrange y = arctan(x) as tan(y) = x.
Step 2: Use implicit differentiation to differentiate this with respect to x, which gives us:
<...
Sin^2(x) cannot be integrated in its current form so you must use trigonometric identities to change sin^2(x) into something else.
Use the formula for cox(2x): cos(2x)=cos(x+x)=cos^2(x)-s...
a.) dy/dx+10x^4+20x^3
d^2y/dx^2=40x^3+60x^2
b.)sub in x=-1 to dy/dx=10(-1)^4+20(-1)^3
=-10
therefore, decreasing
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