what is the derivative of x^4+5x^3-3x^2+12x-4?

Question

i keep using ax^n=nax^(n-1) but it isnt working

Answer 1

This is a very simple derivative and you have the correct equation, I'm not sure what you're having trouble with. Let me break it down for you instead of just giving you the answer so you may be able to see where you went wrong.

You have 5 numbers that you are adding/subtracting:
x^4, 5x^3,3x^2,12x, and 4

The equation for these is ax*n=nax^(n-1)
For x^4, a=1, n=4.
nax^(n-1) = (4)(1)x^(4-1)=4x^3
Similarly with the next two numbers.
For 12x, a=12, n=1.
nax^(n-1) = (1)(12)x^(1-1)=12
And finally for 4, a=4 and n=0 (x^0=1)
nax^(n-1) = (0)(4) = 0.

Add or subtract the derivatives in the original equation and you have 4x^3 + 15x^2 - 6x + 12. In words, all you're doing for these is multiplying the number by the exponent and decreasing the value of the exponent by 1. Hence, for constant numbers (like the 4), they will just disappear (since they are multiplied by exponent of the x, which would have to be 0). Hope that clarifies it for you, as these are the easiest types of derivatives you will see, and you will not need that formula after a little while of working with them.

Answer 2

Quadratic formulation is: x = -b +- ?b^2 - 4ac / 2a 3x^2 + 12x = -4 upload 4 to the two facets. 3x^2 + 12x + 4 = 0 ax^2 + bx + c = 0 a = 3 b = 12 c = 4 -12 +- ?12^2 - 4(3)(4) / 2(3) = -12 +- ?a hundred and forty four - 40 8 / 6 = -12 +- ?ninety six / 6 = -12 +- 4?6 / 6 = -2 +- 4?6 x = -2 - 4?6 x= -2 + 4?6

Answer 3

Make sure you get the signs and products right.

d/dx = 4x^3 + 15x^2 - 6x + 12

Answer 4

4x^3+15x^2-6x+12