Question

Problem 4: Differentiate the following functions using the product rule. You HAVE TO show all the steps as in the example below: Example: Differentiate f(x) = (4x^3 + x^{10})e^{5x} df/dx = (4x^3+x^{10})'e^{5x}+(4x^3+x^{10})(e^{5x})' = (12x^2+10x^9)e^{5x} + (4x^3+x^{10})(5e^{5x}) (a) f(x) = (x^4-8^x)(e^{3x}-3x^5) (b) g(x) = 8^{-4x}(x^6+ln(x)) (c) w(x) = (6ln(x)+7sqrt{x})3^{-x}

          Problem 4: Differentiate the following functions using the product rule.
You HAVE TO show all the steps as in the example below:
Example: Differentiate f(x) = (4x^3 + x^{10})e^{5x}
df/dx = (4x^3+x^{10})'e^{5x}+(4x^3+x^{10})(e^{5x})' = (12x^2+10x^9)e^{5x} + (4x^3+x^{10})(5e^{5x})
(a) f(x) = (x^4-8^x)(e^{3x}-3x^5)
(b) g(x) = 8^{-4x}(x^6+ln(x))
(c) w(x) = (6ln(x)+7sqrt{x})3^{-x}

Problem 4: Differentiate the following functions using the product rule.
You HAVE TO show all the steps as in the example below:
Example: Differentiate f(x) = (4x^3 + x^10)e^5x
df/dx = (4x^3+x^10)'e^5x+(4x^3+x^10)(e^5x)' = (12x^2+10x^9)e^5x + (4x^3+x^10)(5e^5x)
(a) f(x) = (x^4-8^x)(e^3x-3x^5)
(b) g(x) = 8^-4x(x^6+ln(x))
(c) w(x) = (6ln(x)+7sqrtx)3^-x

Added by Susan T.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Sri K

09/28/2022

Step 1

Step 1:** Apply the product rule to differentiate the function \(f(x) = x^4 - 8x^2e^{3x} - 3x^5\): \[f'(x) = (x^4)' - (8x^2)'(e^{3x}) - (3x^5)'\] ** Show more…

Show all steps

Thanks for your feedback!

Problem 4: Differentiate the following functions using the product rule. You HAVE TO show all the steps as in the example below: Example: Differentiate f(x) = (4x^3 + x^{10})e^{5x}