# Step-by-step Solution

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## Step-by-step explanation

Problem to solve:

$\frac{d}{dx}\left(4\sec\left(x\right)-2\csc\left(x\right)\right)$

Learn how to solve sum rule of differentiation problems step by step online.

$\frac{d}{dx}\left(4\sec\left(x\right)\right)+\frac{d}{dx}\left(-2\csc\left(x\right)\right)$

Learn how to solve sum rule of differentiation problems step by step online. Find the derivative (d/dx)(4sec(x)-2csc(x)) using the sum rule. The derivative of a sum of two functions is the sum of the derivatives of each function. The derivative of a function multiplied by a constant (4) is equal to the constant times the derivative of the function. The derivative of a function multiplied by a constant (-2) is equal to the constant times the derivative of the function. Taking the derivative of secant function: \frac{d}{dx}\left(\sec(x)\right)=\sec(x)\cdot\tan(x)\cdot D_x(x).

$4\sec\left(x\right)\tan\left(x\right)+2\csc\left(x\right)\cot\left(x\right)$
$\frac{d}{dx}\left(4\sec\left(x\right)-2\csc\left(x\right)\right)$

### Main topic:

Sum rule of differentiation

### Time to solve it:

~ 0.04 s (SnapXam)