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

The derivative of (sin^2(x)/(sin(x^2))) is sin(2x)csc(x^2)-2xsin^2(x)cot(x^2)csc(x^2)

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

The first derivative of (sin^2(x)/(sin(x^2))) is sin(2x)csc(x^2)-2xsin^2(x)cot(x^2)csc(x^2)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

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

sin (2 x) csc (x^{2}) - 2 x sin^{2} (x) cot (x^{2}) csc (x^{2})

Solution steps

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

Simplify

\frac{sin ^{2} ( x )}{sin ( x ^{2} )} : sin^{2} (x) csc (x^{2})

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

Apply the Product Rule:

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

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

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

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

\frac{d}{d x} (csc (x^{2})) = - cot (x^{2}) csc (x^{2}) \cdot 2 x

= sin (2 x) csc (x^{2}) + (- cot (x^{2}) csc (x^{2}) \cdot 2 x) sin^{2} (x)

Simplify

= sin (2 x) csc (x^{2}) - 2 x sin^{2} (x) cot (x^{2}) csc (x^{2})

\int_{0}^{π} sec (x) d x

\int cos (x) \cdot sin^{3} (x) d x

\int_{0}^{1} \frac{- 7 y}{e ^{2 y}} d y

e^{- 10 t}

\int_{0}^{π} cos^{2} (x) sin (x) d x

What is the derivative of (sin^2(x)/(sin(x^2))) ?
The derivative of (sin^2(x)/(sin(x^2))) is sin(2x)csc(x^2)-2xsin^2(x)cot(x^2)csc(x^2)
What is the first derivative of (sin^2(x)/(sin(x^2))) ?
The first derivative of (sin^2(x)/(sin(x^2))) is sin(2x)csc(x^2)-2xsin^2(x)cot(x^2)csc(x^2)