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

The derivative of (sin(2x)/(cos(x^2))) is cos(2x)*2sec(x^2)+sec(x^2)tan(x^2)*2xsin(2x)

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

The first derivative of (sin(2x)/(cos(x^2))) is cos(2x)*2sec(x^2)+sec(x^2)tan(x^2)*2xsin(2x)

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\frac{d}{d x} (\frac{sin ( 2 x )}{cos ( x ^{2} )})

cos (2 x) \cdot 2 sec (x^{2}) + sec (x^{2}) tan (x^{2}) \cdot 2 x sin (2 x)

Solution steps

\frac{d}{d x} (\frac{sin ( 2 x )}{cos ( x ^{2} )})

Simplify

\frac{sin ( 2 x )}{cos ( x ^{2} )} : sin (2 x) sec (x^{2})

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

Apply the Product Rule:

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

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

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

\frac{d}{d x} (sin (2 x)) = cos (2 x) \cdot 2

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

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

\int - \frac{1}{z ^{2}} d z

\frac{1}{4 s ^{3}} - \frac{5}{3 s ^{2}}

t

y^{^{'}} = x^{2} (1 + y^{2})

What is the derivative of (sin(2x)/(cos(x^2))) ?
The derivative of (sin(2x)/(cos(x^2))) is cos(2x)*2sec(x^2)+sec(x^2)tan(x^2)*2xsin(2x)
What is the first derivative of (sin(2x)/(cos(x^2))) ?
The first derivative of (sin(2x)/(cos(x^2))) is cos(2x)*2sec(x^2)+sec(x^2)tan(x^2)*2xsin(2x)