What is the derivative of 12sin(xsec^2(x)) ?

The derivative of 12sin(xsec^2(x)) is 12sec(x)(1+2tan^2(x))

What is the first derivative of 12sin(xsec^2(x)) ?

The first derivative of 12sin(xsec^2(x)) is 12sec(x)(1+2tan^2(x))

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\frac{d}{d x} (12 sin (x) sec^{2} (x))

12 sec (x) (1 + 2 tan^{2} (x))

Solution steps

\frac{d}{d x} (12 sin (x) sec^{2} (x))

Take the constant out:

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

= 12 \frac{d}{d x} (sin (x) sec^{2} (x))

Apply the Product Rule:

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

f = sin (x), g = sec^{2} (x)

= 12 (\frac{d}{d x} (sin (x)) sec^{2} (x) + \frac{d}{d x} (sec^{2} (x)) sin (x))

\frac{d}{d x} (sin (x)) = cos (x)

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

= 12 (cos (x) sec^{2} (x) + 2 sec^{2} (x) tan (x) sin (x))

Simplify

12 (cos (x) sec^{2} (x) + 2 sec^{2} (x) tan (x) sin (x)) : 12 sec (x) (1 + 2 tan^{2} (x))

= 12 sec (x) (1 + 2 tan^{2} (x))

\int (4 x^{3} - \frac{3}{x ^{3}}) d x

\int \frac{x - 2}{x + 1} d x

\frac{\partial}{\partial x} ((x - 3)^{3})

\frac{d}{d x} (x^{4} - 5 + x^{- 2} + 41 x^{- 4})

y^{^{''}} + 4 y = 2 sin (2 t)

What is the derivative of 12sin(xsec^2(x)) ?
The derivative of 12sin(xsec^2(x)) is 12sec(x)(1+2tan^2(x))
What is the first derivative of 12sin(xsec^2(x)) ?
The first derivative of 12sin(xsec^2(x)) is 12sec(x)(1+2tan^2(x))