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How to differentiate y=x^3+4x+1 when x=3

First of all you calculate dy/dx. To do this you look at each x individually. For the first x you multiply it by it's power and then minus 1 from the power to get 3x^2. Then multiply the next x by the power ...
LS
Answered by Leana S. • Maths tutor
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differentiate with respect to x: (x^3)(e^x)

because the equation is made up of two functions we can think of them separately when differentiating:f(x)= x^3 f'(x)= 3x^2g(x)= e^x g'(x)= e^xdy/dx= (3x^2 e^x)+ (x^3 e^x)
JS
Answered by Jake S. • Maths tutor
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g(x) = x/(x+3) + 3(2x+1)/(x^2 +x - 6) a)Show that g(x) =(x+1)/(x-2), x>3 b)Find the range of g c)Find the exact value of a for which g(a)=g^(-1)(a).

a) First, we need to factorize (x 2 +x-6) = (x-2)(x+3). Therefore, g(x) = x/(x+3) + 3(2x+1)/(x-2)(x+3) = x(x-2)/(x-2)(x+3) + 3(2x+1)/(x-2)(x+3) = (x 2 -2x + 6x +3)/(x-2)(x+3) = (x 2 +4x+3)/(x-2)(x+3).Now we ...
TM
Answered by Teodora M. • Maths tutor
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Find the integral of ((2(7x^(2)-xe^(-2x))-5)/x) . Given that y=27 at x=1, solve the differential equation dy/dx=((2(7x^(2)-xe^(-2x))-5)/-3x).y^(2/3) in terms of y.

Part A)Expand numerator in the integral to get 14x^(2) - 2xe^(-2x)-5Now divide by denominator to get 14x - 2e^(-2x) - 5/xNow integrate to get 7x^(2) + e^(-2x) - 5ln(x)Part B)Get all components of y on the le...
GR
Answered by George R. • Maths tutor
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Express 1/(1+2x)(1-x) in partial fractions

1/(1+2x)(1-x)=(A/(1+2x))+(B/(1-x))1=A(1-x)+B(1+2x) Now set the bracket of one of A or B equal to 0 to get an equation with 1 unknown.Set x=11=A(1-1)+B(1+2(1))1=A(0)+B(3)1=3BB=1/3Set x=-(1/2)1=A(1-(-1/2))+B(1...
LC
Answered by Luke C. • Maths tutor
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