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Find stationary points of curve y = x^3+3x-2

y = x^3+3x-2dy/dx = 3x^2-2Stationary points when dy/dx = 00 = 3x^2-22 = 3x^2+-root2 = 3x+-root2/3 = x
CB
Answered by Charlie B. • Maths tutor
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Find the integers n such that 4^(n)-1 is prime.

4^(n)-1 factors to (2^(n)-1)(2^(n)+1) by difference of two squares by definition of a prime (only has factors 1 and itself (given that itself isn't 1))So Exactly one of the brackets should = 1 for 4^(n)-1 to...
GH
Answered by George H. • Maths tutor
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Given that y = x^2 +2x + 3, find dy/dx.

We use a typical rule for polynomials in the form y = a x b , where a and b are real numbers. Also, for a polynomial equation y = a x b +c x d +.... , dy/dx = d( a x b )/dx + d(c x d )/dx + ...With this info...
JC
Answered by Jamie C. • Maths tutor
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How to differentiate e^x . sin(x)

e x sin(x) is a product of two functions: e x and sin(x). This means we can use the product rule. Let e x = u and sin(x) = v The differential of uv is u'v + v'u where u' and v' are the two functions differen...
BW
Answered by Brent W. • Maths tutor
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differentiate with respect to x : y = x^2 -5x

to find dy/dx, multiply each item by the power of the x, and then decrease the power of the x by 1.Step 1 : 2 x^2 -1 5x (multiplying by power of x)Step 2 : 2 x^1 -1 5x^0Therefore:dy/dx = 2x - 5.
BA
Answered by Branwen A. • Maths tutor
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