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

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

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

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

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

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

Solution steps

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

Simplify

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

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

Apply the Product Rule:

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

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

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

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

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

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

\int x^{4} \cdot e^{- 6 x^{5}} d x

\frac{d}{d x} (tan (x^{7}))

\frac{d}{d x} (8 sin^{3} (x))

\int (8 x + 4) e^{(x^{2} + x)} d x

f (x) = x^{2} - tan (x)

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