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Answer :
Final answer:
The derivative of f(x) = 3(7x^7 - 9x^8)^16 using the chain rule is 0.
Explanation:
To find the derivative of the given function f(x) = 3(7x^7 - 9x^8)^16 using the chain rule, we need to differentiate the outer function and the inner function separately.
Let's start by differentiating the outer function:
- Take the derivative of the constant term 3, which is 0.
- Apply the power rule to the expression (7x^7 - 9x^8)^16. The power rule states that if we have a term raised to a power, we can bring down the power as a coefficient and subtract 1 from the exponent.
Applying the power rule, we get:
f'(x) = 0 * (7x^7 - 9x^8)^15 * (7 * 7x^6 - 8 * 9x^7)
Simplifying further:
f'(x) = 0 * (7x^7 - 9x^8)^15 * (49x^6 - 72x^7)
Since the derivative of the constant term 3 is 0, the derivative of the given function f(x) is 0.
Learn more about using the chain rule to find the derivative here:
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Final answer:
The derivative of f(x) = 3(7x^7 - 9x^8)^16 using the chain rule is 0.
Explanation:
To find the derivative of the given function f(x) = 3(7x^7 - 9x^8)^16 using the chain rule, we need to differentiate the outer function and the inner function separately.
Let's start by differentiating the outer function:
- Take the derivative of the constant term 3, which is 0.
- Apply the power rule to the expression (7x^7 - 9x^8)^16. The power rule states that if we have a term raised to a power, we can bring down the power as a coefficient and subtract 1 from the exponent.
Applying the power rule, we get:
f'(x) = 0 * (7x^7 - 9x^8)^15 * (7 * 7x^6 - 8 * 9x^7)
Simplifying further:
f'(x) = 0 * (7x^7 - 9x^8)^15 * (49x^6 - 72x^7)
Since the derivative of the constant term 3 is 0, the derivative of the given function f(x) is 0.
Learn more about using the chain rule to find the derivative here:
https://brainly.com/question/29498741
#SPJ14
