Find dy/dx for the following functions: a) y = x2+2/x+1, b) y=x2-1/x2+2, c) y = x/(x+4)3, d) y = 3xtx, e) y…

Question

Find dy/dx for the following functions: a) y = x2+2/x+1, b) y=x2-1/x2+2, c) y = x/(x+4)3, d) y = 3xtx, e) y = sqrt(x2-1), f) y = x2/sqrt(x+1), g) y = 1/(x+4)3, h) y = 1/(sqrt(2x−4)2)

ScanSolve AI Tutor · Accepted Answer

Sawa Shari, hebu tuendelee na tatizo (o).

Ili kutatua tatizo (o), tutatumia kanuni ya mnyororo na kanuni ya nguvu.

Tatizo ni:

y = \frac{1}{(3x-4)^2}

Andika upya usemi kwa kutumia kiashiria cha nguvu hasi.
$y = (3x-4)^{-2}$
Tumia kanuni ya mnyororo.
Acha $u = 3x-4$ . Kisha $y = u^{-2}$ .
Tafuta $\frac{du}{dx}$ :
$\frac{du}{dx} = \frac{d}{dx}(3x-4) = 3$
Tafuta $\frac{dy}{du}$ :
$\frac{dy}{du} = \frac{d}{du}(u^{-2}) = -2u^{-2-1} = -2u^{-3}$
Tumia kanuni ya mnyororo $\frac{dy}{dx} = \frac{dy}{du} \cdot \frac{du}{dx}$ .
Badilisha $u$ na $\frac{du}{dx}$ :
$\frac{dy}{dx} = (-2u^{-3})(3)$ $\frac{dy}{dx} = -6u^{-3}$
Badilisha $u$ na usemi wake wa asili $(3x-4)$ .
$\frac{dy}{dx} = -6(3x-4)^{-3}$
Andika jibu kwa kutumia kiashiria cha nguvu chanya.
$\frac{dy}{dx} = -\frac{6}{(3x-4)^3}$
Jibu la mwisho ni:
$\boxed{\frac{dy}{dx} = -\frac{6}{(3x-4)^3}}$

Find dy/dx for the following functions: a) y = x2+2/x+1, b) y=x2−1/x2+2, c) y = x/(x+4)3, d) y = 3xtx, e) y = sqrt(x2−1), f) y = x2/sqrt(x+1), g) y = 1/(x+4)3, h) y = 1/(sqrt(2x-4)2)

Step-by-step solution

Andika upya usemi kwa kutumia kiashiria cha nguvu hasi.

Tumia kanuni ya mnyororo.

Tumia kanuni ya mnyororo $\frac{dy}{dx} = \frac{dy}{du} \cdot \frac{du}{dx}$ .

Badilisha $u$ na usemi wake wa asili $(3x-4)$ .

Andika jibu kwa kutumia kiashiria cha nguvu chanya.

Still stuck on this one?

More Mathematics Questions