Final answer:
To differentiate the function 6x⁵ +4x³ −3x² +2x−7, apply the power rule of differentiation to each term in the function. Therefore, the derivative of the entire function is: 30x⁴ + 12x² - 6x + 2.
Step-by-step explanation:
To differentiate the function 6x⁵ +4x³ −3x² +2x−7, we can apply the power rule of differentiation. The power rule states that if we have a term of the form ax^n, the derivative is given by multiplying the coefficient by the exponent and subtracting 1 from the exponent. Applying this rule to each term in the function, we get:
6x⁵: The derivative is 30x⁴.
4x³: The derivative is 12x².
-3x²: The derivative is -6x.
2x: The derivative is 2.
The derivative of the constant term -7 is 0. Therefore, the derivative of the entire function is: 30x⁴ + 12x² - 6x + 2.