Question

derivative of (7x+6tanx)x*5​

Answer 1

Answer:

Step-by-step explanation:

Formula used:

Product rule of differrentiation:

Given:

Differentiate with respect to x

Answer 2

Given:

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

$\to\sf{y =7x^6 + 6x^5.tanx }$

Things to remember:

$\blacksquare\:\sf{ \dfrac{d(x^n)}{dx}= n x ^{n-1}}$

Product rule:

$\blacksquare\:\sf{\dfrac{d(uv)}{dx}= u.\dfrac{d(v)}{dx}+v.\dfrac{d(u)}{dx}}$

Solution:

$\to\sf{\dfrac{dy}{dx} =7\dfrac{d(x^6 )}{dx} + 6.\bigg[ x^5.\dfrac{d(tanx )}{dx} + tanx \dfrac{d(x^5 )}{dx}\bigg]}$

$\to\sf{\dfrac{dy}{dx}=7.6x^5 + 6.\bigg[ x^5.sec^2x + tanx .5x^4 \bigg]}$

$\to\sf{\dfrac{dy}{dx} =42x^5 + 6.\bigg[ x^5sec^2x + 5x^4tanx \bigg]}$

$\to\boxed{\sf{\red{\dfrac{dy}{dx} =42x^5 + 6x^5sec^2x + 30x^4tanx }}}$