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Show that 12coshx - 4sinhx = 4e^x + 8e^-x

Using the definitions of coshx and sinhx (coshx=1/2(e^x+e^-x) and sinhx=1/2(e^x-e^-x)), we can substitute these into what we want to show, giving 12(1/2(e^x+e^-x)) - 4(1/2(e^x-e^x)), expanding this out gives...
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Answered by Emily W. • Maths tutor
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Mechanics (M1): Particle moving on a straight line with constant acceleration (Relationships of the 5 Key Formulae)

For M1, it is essential for you to be able to solve questions that involve particles moving in a straight line with constant acceleration. The representation of symbols is listed as follow: S - Displacement ...
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Answered by Wai Man C. • Maths tutor
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Differentiate 2x^3+23x^2+3x+5 and find the values of x for which the function f(x) is at either at a maximum or minimum point. (Don't need to specify which is which)

f(x)=2x 3 +23x 2 +3x+5 f'(x)=6x 2 +46x+3 Maximum or minimum when f'(x)=0 6x 2 +46x+3=0 Using the Quadratic Formula: x=(-b+-squareroot(b 2 -4ac))/2a x 1 =-0.0658 x 2 =-7.6
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Answered by Sanjana K. • Maths tutor
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Find f(x^(1/2)+4)dx (Where f is the integral sign)

The general form for an integrand if the integral is of the form f(x^n)dx is (1/(n+1)) * x^(n+1) +c This is applied to each term in the question, remembering the constant in the integrand: So: f(6x+x^(1/2)+4...
MA
Answered by Michael A. • Maths tutor
3705 Views

A curve has the equation y = 4x^3 . Differentiate with respect to y.

y = 4x 3 To differentiate you must find dy/dx. To calculate dy/dx, look at this example using just letters from algebra: y = ax b dy/dx = (ab)x (b-1) As you can see, to calculate dy/dx you must multiply the ...
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Answered by Samuel H. • Maths tutor
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