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Popular >

derivative of (sin(x)(tan(x)))

Solution

\frac{d}{d 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 from-infinity to 12 of re^{r/4}

\int_{- \infty}^{12} r e^{\frac{r}{4}} d r

y^{^{''}} + 10 y = 0

integral of (17x^7)/(315)

\int \frac{17 x ^{7}}{315} d x

integral of (cos(x))/3

\int \frac{cos ( x )}{3} d x

derivative of (x^2-x+1^3)

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

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))