Find dy/dx when y equals:
a) 8x^2 +7x+12
b) 5+4x-5x^2
could you also please show all steps taken, thanks in advance :)
a) 8x^2 +7x+12
b) 5+4x-5x^2
could you also please show all steps taken, thanks in advance :)
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Derivatives are relatively simple. You simply multiply the variable by the given power, then reduce the power by 1. For example, given:
x^a
the derivative would be:
a * x^(a-1)
A practical example would be:
2x^5
the derivative is:
5 * 2x^(5-1) = 10x^4
a) 8x^2 + 7x + 12
derivative = 16x + 7
To get this, we have:
2*8x^(2-1) + 1*7x^(1-1) + 0*12x^(0-1) =
16x^1 + 7x^0 + 0 (note that x^0 = 1, all constants simply disappear when taking a derivative. In other words, the derivative of ANY constant = 0)
16x + 7
b) 5 + 4x - 5x^2
derivative is:
0 + 4 - 10x =
4 - 10x
Best of luck!
x^a
the derivative would be:
a * x^(a-1)
A practical example would be:
2x^5
the derivative is:
5 * 2x^(5-1) = 10x^4
a) 8x^2 + 7x + 12
derivative = 16x + 7
To get this, we have:
2*8x^(2-1) + 1*7x^(1-1) + 0*12x^(0-1) =
16x^1 + 7x^0 + 0 (note that x^0 = 1, all constants simply disappear when taking a derivative. In other words, the derivative of ANY constant = 0)
16x + 7
b) 5 + 4x - 5x^2
derivative is:
0 + 4 - 10x =
4 - 10x
Best of luck!
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f(x) = au^n
f '(x) = (a) (n) u^(n-1)
a) 8x^2 +7x+12
dy/dx = 8(2)(x^1) + 7 = 16x + 7
b) 5 + 4x + (-5x^2)
dy/dx = 4 + (-5)(2)(x^1) = 4 - 10x
f '(x) = (a) (n) u^(n-1)
a) 8x^2 +7x+12
dy/dx = 8(2)(x^1) + 7 = 16x + 7
b) 5 + 4x + (-5x^2)
dy/dx = 4 + (-5)(2)(x^1) = 4 - 10x
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a) =(2*8)X + 7
=16X + 7
b) =4 - (5*2)X
=4 - 10X
=16X + 7
b) =4 - (5*2)X
=4 - 10X
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a)-
dy/dx=16x+7
b)-
dy/dx=4-10x
maybe!!!
dy/dx=16x+7
b)-
dy/dx=4-10x
maybe!!!