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Question 13 Compute the derivative of the following function. f(x) = (2x^2 + 3)^2 e^{6x} f'(x) = 2e^{6x}(12x^4 + 8x^3 + 36x^2 + 12x + 27) f'(x) = 2e^{6x}(4x^2 + 6) f'(x) = e^{6x}(4x^4 + 8x^3 + 12x^2 + 4x + 9) f'(x) = 2e^{6x}(2x^2 + 3)^2 f'(x) = 2e^{6x}(16x^4 + 24x + 9)

          Question 13
Compute the derivative of the following function. f(x) = (2x^2 + 3)^2 e^{6x}
f'(x) = 2e^{6x}(12x^4 + 8x^3 + 36x^2 + 12x + 27)
f'(x) = 2e^{6x}(4x^2 + 6)
f'(x) = e^{6x}(4x^4 + 8x^3 + 12x^2 + 4x + 9)
f'(x) = 2e^{6x}(2x^2 + 3)^2
f'(x) = 2e^{6x}(16x^4 + 24x + 9)

Question 13
Compute the derivative of the following function. f(x) = (2x^2 + 3)^2 e^6x
f'(x) = 2e^6x(12x^4 + 8x^3 + 36x^2 + 12x + 27)
f'(x) = 2e^6x(4x^2 + 6)
f'(x) = e^6x(4x^4 + 8x^3 + 12x^2 + 4x + 9)
f'(x) = 2e^6x(2x^2 + 3)^2
f'(x) = 2e^6x(16x^4 + 24x + 9)

Added by Martin S.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Sri K

03/23/2023

Step 1

We will use the product rule for differentiation, which states that if we have a function h(x) = f(x) * g(x), then h'(x) = f'(x) * g(x) + f(x) * g'(x). Let f(x) = (2x^2 + 3)^7 and g(x) = e^(6x). Now, we need to find the derivatives of f(x) and g(x). For f(x), Show more…

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Compute the derivative of the following function: f(x) = (2x^2+3)^2e^(6x) f'(x) = 2e^(6x)(12x^4 + 8x^3 + 36x^2 + 12x + 27) f'(x) = 2e^(6x)(4x^2 + 6) f'(x) = e^(6x)(4x^4 + 8x^3 + 12x^2 + 4x + 9) f'(x) = 2e^(6x)(2x^2 + 3)^2 f'(x) = 2e^(6x)(16x^4 + 24x + 9)