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Answer :
Final answer:
The derivative of the function 7x⁶+8x⁵-3x⁴+11x²+6x+7 with respect to x is 42x⁵+40x⁴-12x³+22x+6, obtained by applying the power rule to each term.
Explanation:
To differentiate the function 7x⁶+8x⁵-3x⁴+11x²+6x+7 with respect to x, we use the power rule of differentiation. This rule states that the derivative of xⁿ, where n is a constant, is nxⁿ⁻¹. Applying this rule to each term:
- The derivative of 7x⁶ is 42x⁵.
- The derivative of 8x⁵ is 40x⁴.
- The derivative of -3x⁴ is -12x³.
- The derivative of 11x² is 22x.
- The derivative of 6x is 6.
- The derivative of 7, a constant, is 0.
Combining all these, the derivative of the given function with respect to x is 42x⁵+40x⁴-12x³+22x+6.
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