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The differential of tan(x) is sec²(x), however knowing how dy/dx tan(x)=sec²(x) is very useful in differentiating other trigonometric functions. So, if we first employ the rule that ...

Rearrange the first equation to get y on its own:   y=-(1+4x) Substitute into the second equation:        (1+4x)(1+4x)+5x^2+2x=0     21x^2+10x+1=0 Substite into the quadratic formula to solve    (-b+/-(b^...

a) To answer this question, one must be familiar with laws of logs, more sprecifically the rules when applied to the natural log of x, and exponentials (e). 2ln(2x+1) - 10 = 0 Step 1) 2ln(2x+1) = 10 Step ...

To do this, first draw a sketch of both graphs to see roughly what kind of result we should expect to get. We know that at the intersection points, the values of x and y for both graphs must be equal. so ...

Here we will use integration by parts because we have the product of two terms, x and 2^x. Using the integration by parts formula, we have to differentiate one of these terms and integrate the other. We c...