What is the derivative of sec(5x+1) ?

The derivative of sec(5x+1) is 5sec(5x)tan(5x)

What is the first derivative of sec(5x+1) ?

The first derivative of sec(5x+1) is 5sec(5x)tan(5x)

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\frac{d}{d x} (sec (5 x) + 1)

5 sec (5 x) tan (5 x)

Solution steps

\frac{d}{d x} (sec (5 x) + 1)

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{d}{d x} (sec (5 x)) + \frac{d}{d x} (1)

\frac{d}{d x} (sec (5 x)) = sec (5 x) tan (5 x) \cdot 5

\frac{d}{d x} (1) = 0

= sec (5 x) tan (5 x) \cdot 5 + 0

Simplify

= 5 sec (5 x) tan (5 x)

f (x) = 4 x^{\frac{5}{4}} + 4 x^{\frac{3}{2}} + 8 x

(x - 1)^{3} \frac{d y}{d x} + 4 (x - 1)^{2} y = x + 1

y^{^{'}} = - \frac{1 + x + y}{1 + x}

\int \frac{cos ( 6 x )}{1 + sin ^{2} ( 6 x )} d x

\int \frac{1}{9 - 5 x} d x

What is the derivative of sec(5x+1) ?
The derivative of sec(5x+1) is 5sec(5x)tan(5x)
What is the first derivative of sec(5x+1) ?
The first derivative of sec(5x+1) is 5sec(5x)tan(5x)