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Popular >

derivative of f(x)=sin(x)tan(x)

Solution

derivative of

f (x) = 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

integral of sin^4(1/2)x

\int sin^{4} (\frac{1}{2}) x d x

integral of (3x+15)sqrt(x^2+10x+4)

\int (3 x + 15) x^{2} + 10 x + 4 d x

integral of (e^{2t})

\int (e^{2 t}) d t

derivative of (sin(3x))/(tan(4x))derivative of

\frac{sin ( 3 x )}{tan ( 4 x )}

taylor 1/(x-1),21 taylor

\frac{1}{x - 1}, 21

Frequently Asked Questions (FAQ)

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