Question

what is the derivative of tan 4x +5​

Answer 1

Derivative of tan(4x+5) is 4.sec²(4x+5)

Given

tan ( 4x + 5 )

To Find

Derivative

Solution

Let , y = tan ( 4x + 5 )

Differentiate with respect to x on both sides , we get ,

$\to \rm \dfrac{dy}{dx}=\dfrac{d}{dx}(\tan (4x+5))\\\\\to \rm \dfrac{dy}{dx}=sec^2(4x+5)\dfrac{d}{dx}(4x+5)\\\\\to \rm \dfrac{dy}{dx}=sec^2(4x+5)(4)\\\\\to \bf \pink{\dfrac{dy}{dx}=4sec^2(4x+5)\ \; \bigstar}$

So , Derivative of tan (4x+5) is 4.sec²(4x+5)

Answer 2

Derivative of tan(4x+5) is 4.sec²(4x+5)

Given:

tan ( 4x + 5 )

To Find:

Derivative

Solution:

Let , y = tan ( 4x + 5 )

Differentiate with respect to x on both sides , we get ,

$\begin{gathered}\to \rm \dfrac{dy}{dx}=\dfrac{d}{dx}(\tan (4x+5))\\\\\to \rm \dfrac{dy}{dx}=sec^2(4x+5)\dfrac{d}{dx}(4x+5)\\\\\to \rm \dfrac{dy}{dx}=sec^2(4x+5)(4)\\\\\to \bf \green{\dfrac{dy}{dx}=4sec^2(4x+5)\ \; \bigstar}\end{gathered}$

$\boxed{So , Derivative of tan (4x+5) is 4.sec²(4x+5)}$