Calculus Examples

$\int \sec (y) (\tan (y) - \sec (y)) d y$

Step 1

Apply the distributive property.

$\frac{d}{d x} [\int \sec (y) \tan (y) + \sec (y) (- \sec (y)) d y]$

Step 2

Rewrite using the commutative property of multiplication.

$\frac{d}{d x} [\int \sec (y) \tan (y) - \sec (y) \sec (y) d y]$

Step 3

Multiply $- \sec (y) \sec (y)$ .

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Step 3.1

Raise $\sec (y)$ to the power of $1$ .

$\frac{d}{d x} [\int \sec (y) \tan (y) - (\sec^{1} (y) \sec (y)) d y]$

Step 3.2

Raise $\sec (y)$ to the power of $1$ .

$\frac{d}{d x} [\int \sec (y) \tan (y) - (\sec^{1} (y) \sec^{1} (y)) d y]$

Step 3.3

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\frac{d}{d x} [\int \sec (y) \tan (y) - {\sec (y)}^{1 + 1} d y]$

Step 3.4

Add $1$ and $1$ .

$\frac{d}{d x} [\int \sec (y) \tan (y) - \sec^{2} (y) d y]$

Step 4

Since $\int \sec (y) \tan (y) - \sec^{2} (y) d y$ is constant with respect to $x$ , the derivative of $\int \sec (y) \tan (y) - \sec^{2} (y) d y$ with respect to $x$ is $0$ .

$0$