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Popular >

derivative of sin(x*tan(x))

Solution

\frac{d}{d x} (sin (x) \cdot 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

(dx)/(dt)=ax-bx^2-0

\frac{d x}{d t} = a x - b x^{2} - 0

derivative of (2x^2+4x+2)/(sqrt(x))derivative of

\frac{2 x ^{2} + 4 x + 2}{x}

tangent of y=4x^3-4x tangent of

y = 4 x^{3} - 4 x

integral from-1 to 1 of 1/(x^{1/3)}

\int_{- 1}^{1} \frac{1}{x ^{\frac{1}{3}}} d x

integral from 0 to infinity of e^{-bt}

\int_{0}^{\infty} e^{- b t} d t

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))