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

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

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

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

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\frac{d}{d x} (- (x - \frac{π}{2}) tan (x))

- tan (x) - x sec^{2} (x) + \frac{π}{2} sec^{2} (x)

Solution steps

\frac{d}{d x} (- (x - \frac{π}{2}) tan (x))

Take the constant out:

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

= - \frac{d}{d x} ((x - \frac{π}{2}) tan (x))

Apply the Product Rule:

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

f = x - \frac{π}{2}, g = tan (x)

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

\frac{d}{d x} (x - \frac{π}{2}) = 1

\frac{d}{d x} (tan (x)) = sec^{2} (x)

= - (1 \cdot tan (x) + sec^{2} (x) (x - \frac{π}{2}))

Simplify

- (1 \cdot tan (x) + sec^{2} (x) (x - \frac{π}{2})) : - tan (x) - x sec^{2} (x) + \frac{π}{2} sec^{2} (x)

= - tan (x) - x sec^{2} (x) + \frac{π}{2} sec^{2} (x)

\int_{0}^{\frac{1}{2}} arcsin (x) d x

\int \frac{e ^{- x}}{x ^{3}} d x

\int 9 tan^{3} (2 x) sec^{5} (2 x) d x

\int_{- 5}^{5} 1 + x^{2} d x

(e^{y})^{^{'}}

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