Question

To obtain the final expression for $f'(t)$, simplify the expression. $f'(t) = \frac{t^6(-\sin t) - \cos t(6t^5)}{(t^6)^2}$ $= -\frac{t^6(\sin t) + \cos t(6t^5)}{t^6\sin(t) + 6t^5\cos(t)}$ $= -\frac{t^6\sin(t) + 6t^5\cos(t)}{t^{12}}$

Name: to obtain the final expression for ft simplify the expression ft fract6 sin t cos t6t5t62 fract6sin t cos t6t5t6sint 6t5cost fract6sint 6t5costt12 47342
Uploaded: 2023-05-12T13:31:41-08:00
Duration: 3 min 16 s
Channel: Madhur L
Description: to obtain the final expression for ft simplify the expression ft fract6 sin t cos t6t5t62 fract6sin t cos t6t5t6sint 6t5cost fract6sint 6t5costt12 47342

          To obtain the final expression for $f'(t)$, simplify the expression.
$f'(t) = \frac{t^6(-\sin t) - \cos t(6t^5)}{(t^6)^2}$
$= -\frac{t^6(\sin t) + \cos t(6t^5)}{t^6\sin(t) + 6t^5\cos(t)}$
$= -\frac{t^6\sin(t) + 6t^5\cos(t)}{t^{12}}$

$to obtain the final expression for ft simplify the expression ft fract6 sin t cos t6t5t62 fract6sin t cos t6t5t6sint 6t5cost fract6sint 6t5costt12 47342$

Added by Michael C.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Madhur L

05/12/2023

Step 1

The initial expression is: $f'(t) = \frac{t^6(-\sin t) - \cos t(6t^5)}{(t^6)^2}$ Step 2: Simplify the numerator. $t^6(-\sin t) - \cos t(6t^5) = -t^6\sin t - 6t^5\cos t$ Step 3: Simplify the denominator. $(t^6)^2 = t^{6 \times 2} = t^{12}$ Step 4: Substitute the Show more…

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To obtain the final expression for $f'(t)$, simplify the expression. $f'(t) = \frac{t^6(-\sin t) - \cos t(6t^5)}{(t^6)^2}$ $= -\frac{t^6(\sin t) + \cos t(6t^5)}{t^6\sin(t) + 6t^5\cos(t)}$ $= -\frac{t^6\sin(t) + 6t^5\cos(t)}{t^{12}}$