What is the derivative of 9tan(xsec(x)) ?

The derivative of 9tan(xsec(x)) is 9(-sec(x)+2sec^3(x))

What is the first derivative of 9tan(xsec(x)) ?

The first derivative of 9tan(xsec(x)) is 9(-sec(x)+2sec^3(x))

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\frac{d}{d x} (9 tan (x) sec (x))

9 (- sec (x) + 2 sec^{3} (x))

Solution steps

\frac{d}{d x} (9 tan (x) sec (x))

Take the constant out:

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

= 9 \frac{d}{d x} (tan (x) sec (x))

Apply the Product Rule:

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

f = tan (x), g = sec (x)

= 9 (\frac{d}{d x} (tan (x)) sec (x) + \frac{d}{d x} (sec (x)) tan (x))

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

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

= 9 (sec^{2} (x) sec (x) + sec (x) tan (x) tan (x))

Simplify

9 (sec^{2} (x) sec (x) + sec (x) tan (x) tan (x)) : 9 (- sec (x) + 2 sec^{3} (x))

= 9 (- sec (x) + 2 sec^{3} (x))

\int \frac{1}{1 + 3 x} d x

\frac{5}{4 + x ^{2}}, at x = 2

\int 3 csc^{2} (x) d x

y^{^{'}} + cot (x) y - x e^{x} = 0

\int (2 x + 1) e^{x (x + 1)} d x

What is the derivative of 9tan(xsec(x)) ?
The derivative of 9tan(xsec(x)) is 9(-sec(x)+2sec^3(x))
What is the first derivative of 9tan(xsec(x)) ?
The first derivative of 9tan(xsec(x)) is 9(-sec(x)+2sec^3(x))