Question

differentiation of y=12x^5+3x^4+7x^3+x^2-9x+6

Answer 1

Answer:

This problem is simply a polynomial which can be solved with a combination of Sum and Difference Rule, Multiple Rule and basic derivatives.

dy by dx = d by dx12x5 + d by dx3x4 + d by dx7x3 + d by dxx2 − d by dx9x + d by dx6 by Sum and Difference Rule

dy by dx = 12d by dxx5 + 3d by dxx4 + 7d by dxx3 + d by dxx2 − 9d by dxx + d by dx6 by Multiple Rule

dy by dx = 12(5x4) + 3(4x3) + 7(3x2) + 2x − 9 + 0 by basic derivatives

dy by dx= 60 x4 + 12 x3 + 21 x2 + 2x − 9 by simplifying

i hope that you found it useful

Answer 2

Given:

y' = 12x⁵ + 3x⁴ + 7x³ + x² - 9x + 6

Solution:

Differentiation of y w.r.t. x

y' = dy/dx

y' = d(12x⁵ + 3x⁴ + 7x³ + x² - 9x + 6)/dx

y' = 12 (5x⁴) + 3 (4x³) + 7 (3x²) - 9 + 0

y' = 60x⁴ + 12x³ + 21x² - 9

Therefore, dy/dx = 60x⁴ + 12x³ + 21x² - 9.

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Note:

d(x^n)/dx = nx^(n-1)