derivative of tan(4x+4) — step-by-step solution

Let's perform the differentiation:

\frac{d}{d x} (\tan (4 x + 4))

Apply the differentiation rule:

\frac{d}{d x} (\tan (f)) = \frac{d}{d x} (f) \cdot \frac{1}{{\cos (f)}^{2}}

with f =

4 x + 4

ⓘ The derivative of tan(x) is 1/cos(x)^2:

\frac{d}{d x} (\tan (4 x + 4))

\frac{d}{d x} (4 x + 4) \cdot \frac{1}{{\cos (4 x + 4)}^{2}}

\frac{d}{d x} (4 x + 4) \cdot \frac{1}{{\cos (4 x + 4)}^{2}}

ⓘ The derivative of a sum is the sum of the derivatives:

\frac{d}{d x} (4 x + 4)

\frac{d}{d x} (4 x) + 0

\frac{\frac{d}{d x} (4 x) + 0}{{\cos (4 x + 4)}^{2}}

ⓘ A constant factor stays in front of the derivative, (k*u)' = k*u':

\frac{d}{d x} (4 x)

4

▶Derivative:

\frac{4}{{\cos (4 x + 4)}^{2}}