High School

Use the chain rule to find the derivative.

Given: [tex] f(x) = 3(7x^7 - 9x^8)^{16} [/tex]

Find: [tex] f'(x) [/tex]

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:

  1. Take the derivative of the constant term 3, which is 0.
  2. 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

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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:

  1. Take the derivative of the constant term 3, which is 0.
  2. 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