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

The derivative of (sin^2(x)/(cos(x))) is sin(x)(1+sec^2(x))

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

The first derivative of (sin^2(x)/(cos(x))) is sin(x)(1+sec^2(x))

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

sin (x) (1 + sec^{2} (x))

Solution steps

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

Simplify

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

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

Apply the Product Rule:

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

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

= \frac{d}{d x} (sin (x)) tan (x) + \frac{d}{d x} (tan (x)) sin (x)

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

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

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

Simplify

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

= sin (x) (1 + sec^{2} (x))

(- x + 2), (- x^{2} - 2 x), - 2, - 1

(1 + x)^{- \frac{2}{3}}

y = (1 + 2 x)^{10}, (0, 1)

5 x arcsin (x)

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

What is the derivative of (sin^2(x)/(cos(x))) ?
The derivative of (sin^2(x)/(cos(x))) is sin(x)(1+sec^2(x))
What is the first derivative of (sin^2(x)/(cos(x))) ?
The first derivative of (sin^2(x)/(cos(x))) is sin(x)(1+sec^2(x))