Question

If Y =( 7 x + 6 tan x) x^5 then find dy/dx​

Answer 1

Answer:

$\frac{dy}{dx}=48x^5++6x^5tan^2x+30x^4\:tanx$

Step-by-step explanation:

Formula used:

Product rule of differrentiation:

$\frac{d(uv)}{dx}=u.\frac{dv}{dx}+v.\frac{du}{dx}$

Given:

$y=(7x+6\:tanx)x^5\\\\y=7x^6+6x^5\:tanx$

Differentiate with respect to x

$\frac{dy}{dx}=\frac{d[7x^6+6x^5\:tanx]}{dx}\\\\\frac{dy}{dx}=\frac{d[7x^6]}{dx}+\frac{d[6x^5\:tanx]}{dx}\\\\\frac{dy}{dx}=7\frac{d[x^6]}{dx}+6\frac{d[x^5\:tanx]}{dx}\\\\\frac{dy}{dx}=7(6x^5)+6[x^5\:sec^2x+tanx.5x^4]\\\\\frac{dy}{dx}=42x^5+6x^5\:sec^2x+tanx.30x^4\\\\\frac{dy}{dx}=42x^5+6x^5(1+tan^2x)+tanx.30x^4\\\\\frac{dy}{dx}=42x^5+6x^5+6x^5tan^2x+30x^4\:tanx\\\\\frac{dy}{dx}=48x^5++6x^5tan^2x+30x^4\:tanx$