Question

If y = (7x+6 tan x)x5, then find dy/dx.


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Answer 1

Step-by-step explanation:

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Answer 2

$\displaystyle \bf \frac{dy}{dx} = 6 {x}^{5} (7 + {sec}^{2} x) + 30{x}^{4} tanx$

Given :

$\displaystyle \sf y = (7x + 6 \: tanx) {x}^{5}$

To find :

$\displaystyle \sf \frac{dy}{dx}$

Solution :

Step 1 of 2 :

Write down the given equation

Here the given equation is

$\displaystyle \sf y = (7x + 6 \: tanx) {x}^{5}$

Step 2 of 2 :

$\displaystyle \sf Find \: value \: of \: \frac{dy}{dx}$

$\displaystyle \sf y = (7x + 6 \: tanx) {x}^{5}$

$\displaystyle \sf{ \implies }y = 7 {x}^{6} + 6 {x}^{5} \: tanx$

Differentiating both sides with respect to x we get

$\displaystyle \sf \frac{dy}{dx} = \frac{d}{dx} \bigg(7 {x}^{6} + 6 {x}^{5} \: tanx\bigg)$

$\displaystyle \sf{ \implies }\frac{dy}{dx} = \frac{d}{dx} \bigg(7 {x}^{6} \bigg) + \frac{d}{dx} \bigg( 6 {x}^{5} \: tanx\bigg)$

$\displaystyle \sf{ \implies }\frac{dy}{dx} = 7 \times 6 \times {x}^{6 - 1} +6 \bigg[ {x}^{5} \frac{d}{dx} \bigg( \: tanx\bigg) + tanx\frac{d}{dx} \bigg( {x}^{5} \bigg)\bigg]$

$\displaystyle \sf{ \implies }\frac{dy}{dx} = 42 {x}^{5} +6 {x}^{5} {sec}^{2} x + 30 {x}^{4} tanx$

$\displaystyle \sf{ \implies } \frac{dy}{dx} = 6 {x}^{5} (7 + {sec}^{2} x) + 30{x}^{4} tanx$

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