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Why is the derivative of sin(x), cos(x)?

Find out what they know what the questions means, ie if they know what sinx and cosx are and then how much they understand about what derivatives are.I would explain from the point they're at, define everyth...
RA
Answered by Ryan A. • Maths tutor
4074 Views

f(x) = x^3 + 3x^2 + 5. Find (a) f ′′(x), (b) ∫f(x)dx.

(a) To find the second derivative of f(x) we must differentiate f twice.the first derivative of f is f'(x)= 3x^2 + 6xthe second derivative therefore is f''(x)= 6x +6 (b) The integral of f(x) with respect to ...
SC
Answered by Samraj C. • Maths tutor
8456 Views

Solve, giving your answer to 3 s.f. : 2^(2x) - 6(2^(x) ) + 5 = 0

2 2x - 6(2 x ) + 5 = 0let y = 2 x y 2 - 6y + 5 = 0(y-5)(y-1) = 0 y=5, y=12 x = 5, therefore, x = log 2 5 = 2.32 (3 s.f.)2 x = 1, therefore, x = log 2 1 = 0
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Answered by Jess O. • Maths tutor
5351 Views

Find the gradient of the function f(x,y)=x^3 + y^3 -3xy at the point (2,1), given that f(2,1) = 6.

Firstly, establish that the correct method to do this is via differentiation: specifically implicit differentiation. To find the gradient, we need to find dy/dx . The differential with respect to x of x 3 = ...
DD
Answered by Daniel D. • Maths tutor
6815 Views

If f(x) = sin(2x)/(x^2) find f'(x)

As f(x) is in the form of u(x)/v(x) we can apply the rule that f'(x) = (u'(x)*v(x) - v'(x)*u(x))/(v(x) 2 ), pulled from the C3 formula booklet. If u(x) = sin(2x) then u'(x) = 2cos(2x). If v(x) = x 2 then v'(...
LR
Answered by Leo R. • Maths tutor
4276 Views