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2015年7月28日 · d/dx (2^x) = 2^x * ln2 In order to be able to calculate the derivative of 2^x, you're going to need to use two things the fact that d/dx(e^x) = e^x the chain rule The idea here is that you can use the fact that you know what the derivative of e^x is to try and determine what the derivative of another constant raised to the power of x, in this case equal to 2, is. To do that, …

2016年9月17日 · (x-2)^2=x^2-4x+4 This is an example of the square of a difference, (a-b)^2=a^2-2ab+b^2, where a=x and b=2. Substitute your values into the equ

2018年4月5日 · I=x/sqrt(a^2-x^2)-sin^-1(x/a)+c Here, I=intx^2/((a^2-x^2)^(3/2))dx Let ,x=asint=>dx=acostdt :.a^2-x^2=a^2 ...

2018年1月31日 · Prove: 1- cos(x) = 2sin^2(x/2) Digress, for a moment, to the identity cos(2u) = 1 - 2sin^2(u) Substitute u = x/2: cos(x) = 1-2sin^2(x/2) Add 2sin(x/2)-cos(x) to both sides: 2sin^2(x/2) = 1-cos(x) Return to the original equation and make the above substitution: 1- …

2016年9月18日 · By the chain rule. Letting y = sin^2(u) and u = x/2, we need to differentiate both functions and multiply the derivatives together. The derivative of y = sin^2u can be obtained as follows: y = (sinu)(sinu) By the product rule: y' = cosu xx sinu + cosu xx sinu y' = 2cosusinu y' = sin2u The derivative of u = x/2 can be obtained using the quotient rule: u = x/2 u' = (1 xx 2 - x …

2017年2月9日 · What is the derivative of #f(x)=(log_6(x))^2# ? See all questions in Differentiating Logarithmic Functions without Base e Impact of this question

2016年11月12日 · x_1 = -0.7667 to 4dp x_2= 2 x_3 = 4 > x^2 = 2^x There is no "easy" way to solve this equation. First let us look at the graphs: We can see there is one solution in the interval -1 < x < 0 and a second solution at what appears to be x=2, and a third at what appears to be x=4. The two solution x=2,4 can easily be verified to be exact by substitution. We can find the …

2014年9月8日 · Answer 2sin(x)cos(x) Explanation You would use the chain rule to solve this. To do that, you'll have to determine what the "outer" function is and what the "inner" function composed in the outer function is. In this case, sin(x) is …

2016年2月15日 · Partial fractions of x^2/(x^2+x+2) are 1-(x+2)/(x^2+x+2 As the denominator x^2+x+2 is quadratic and its determinant (-b+-sqrt(b^2-4ac))/(2a) is not rational (as sqrt(b^2-4ac)=sqrt(-7) is not rational), its partial fractions will be of type (Ax+B)/(x^2+x+2). But, degree of numerator is 2 hence let us write x^2/(x^2+x+2) as x^2/(x^2+x+2)=1-(x+2)/(x^2+x+2 Hence …