What is the derivative of (-2x)/(cos(x)) ?

The derivative of (-2x)/(cos(x)) is -2(sec(x)+xsec(x)tan(x))

What is the first derivative of (-2x)/(cos(x)) ?

The first derivative of (-2x)/(cos(x)) is -2(sec(x)+xsec(x)tan(x))

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derivative of

\frac{- 2 x}{cos ( x )}

- 2 (sec (x) + x sec (x) tan (x))

Solution steps

\frac{d}{d x} (\frac{- 2 x}{cos ( x )})

Simplify

\frac{- 2 x}{cos ( x )} : - 2 x sec (x)

= \frac{d}{d x} (- 2 x sec (x))

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

= - 2 \frac{d}{d x} (x sec (x))

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = x, g = sec (x)

= - 2 (\frac{d x}{d x} sec (x) + \frac{d}{d x} (sec (x)) x)

\frac{d x}{d x} = 1

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

= - 2 (1 \cdot sec (x) + sec (x) tan (x) x)

Simplify

= - 2 (sec (x) + x sec (x) tan (x))

\frac{d}{d t} (3 cos^{6} (t))

e^{3} x + 2

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

3 x^{5} + 25 x^{2} - 8 x + 11

\frac{d}{d z} (arcsin (z^{3} - y))

What is the derivative of (-2x)/(cos(x)) ?
The derivative of (-2x)/(cos(x)) is -2(sec(x)+xsec(x)tan(x))
What is the first derivative of (-2x)/(cos(x)) ?
The first derivative of (-2x)/(cos(x)) is -2(sec(x)+xsec(x)tan(x))