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Given that dy/dx=6-8x+x^4 and that x=1 when y=4. Find an expression for y in terms of x.

Fristly, we should integrate the whole equation, y=∫ 6-8x+x^4 dx y=6x-4x^2+x^5/5+C Then, subsitituting values to find the C, 4=6 1-4 1^2+1^5/5+C 4=6-4+1/5+C 4=11/5+C So, C=9/5. Hence, y=6x-4x^2+x^5/5+9/5.
PL
Answered by Paine L. • Maths tutor
6395 Views

Find dy/dx of 5x^2 + 2y^3 +8 =17.

As we have to differentiate both x and y, we must use implict differentiation for the y by differentiating it with respect to x (also written as d/dx) 5x 2 -> 10x (multiply the power by the number at the ...
AP
Answered by Anish P. • Maths tutor
5409 Views

How do I solve an integration by substitution problem?

I think it’s best I work through an example with you as these problems can vary quite a lot, but the general methods used are the same. Example: Use the substitution u=x 2 +5 to find: The integral of (x 3 /s...
AD
Answered by Andrew D. • Maths tutor
7779 Views

Given that y = 5x^2 - 4/(x^3), x not equal to 0, find dy/dx.

y = 5x 2 - 4/x 3 1/x can be written as x -1 , which means our equation can also be written as y = 5x 2 - 4x -3 . dy/dx means that we need to differentiate y in terms of x. To differentiate an equation, we ne...
NL
Answered by Nick12 L. • Maths tutor
8689 Views

Solve the simultaneous equations (with a calculator)

x^2 + y^2 = 9 x + y = 2 1) Firstly look at the second equation which is the simplest and think how you can rearrange it to fit into the first equation: x + y = 2 can be rearranged to y = 2-x 2) y = 2-x can t...
EG
Answered by Emily G. • Maths tutor
18882 Views