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Popular >

derivative of sin(x)tan(x)

Solution

derivative of

sin (x) tan (x)

Solution

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

Solution steps

\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))

Popular Examples

derivative of sqrt(3)cos(5x+sin(5x))

\frac{d}{d x} (3 cos (5 x) + sin (5 x))

integral from 1 to 16 of 1/(2x)

\int_{1}^{16} \frac{1}{2 x} d x

integral of (-x+8)/(-x^2-x+8)

\int \frac{- x + 8}{- x ^{2} - x + 8} d x

limit as x approaches 1 of (1+x)/(1-x)

x \to 1 lim (\frac{1 + x}{1 - x})

taylor 1/(1+1x)taylor

\frac{1}{1 + 1 x}

Frequently Asked Questions (FAQ)

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