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Find the equation of the tangent to the curve y = 4x^2 (x+3)^5 at the point (-1, 128).

y = 4x 2 (x+3) 5 . Use the product rule to find the first derivative of the curve, 8x(x+3) 5 + 20x 2 (x+3) 4 , and substitute x = -1 to find the gradient at the point (-1, 128). This should be 64. Now substi...
JG
Answered by Jack G. • Maths tutor
4021 Views

How do I use the product rule for differentiation?

You should use the product rule when you have a function f(x), which you can't differentiate straight away. But which can be written in the form f(x)=g(x)h(x), where g(x) and h(x) are functions that you do k...
HV
Answered by Harry V. • Maths tutor
3507 Views

y = 4(x^3) + 7x ... Find dy/dx

This is a simple differentiation question. To start, you need to know the general method of differentiation. This is: if y = Axb then dy/dx = (A*b)x b-1 There are two terms to differentiate in this problem, ...
EE
Answered by Emilio E. • Maths tutor
4082 Views

Given that A(sin θ + cos θ) + B(cos θ − sin θ) ≡ 4 sin θ, find the values of the constants A and B.

Since this must be true for all values of θ, and cos and sin are distinct functions, no non-zero multiple of cosθ could ever be equal to 4 sinθ for all values of θ. Therefore, the overall multiple of cosθ on...
DB
Answered by David B. • Maths tutor
8765 Views

Find the derivative with respect to x, of 5cos(x)+ 4sin(x)

f(x) = 5cos(x) + 4sin(x)to find f , (x) this is just another notation for the derivative.To differentiate trigonometry I always use this one simple trick which I will show on the white board better sin cos -...
RP
Answered by Ryan P. • Maths tutor
4983 Views