en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

derivative of x^5sin(xtan(x))

Solution

\frac{d}{d x} (x^{5} sin (x) tan (x))

Solution

5 x^{4} sin (x) tan (x) + sin (x) (1 + sec^{2} (x)) x^{5}

Solution steps

\frac{d}{d x} (x^{5} sin (x) tan (x))

Apply the Product Rule:

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

f = x^{5}, g = sin (x) tan (x)

= \frac{d}{d x} (x^{5}) sin (x) tan (x) + \frac{d}{d x} (sin (x) tan (x)) x^{5}

\frac{d}{d x} (x^{5}) = 5 x^{4}

\frac{d}{d x} (sin (x) tan (x)) = sin (x) (1 + sec^{2} (x))

= 5 x^{4} sin (x) tan (x) + sin (x) (1 + sec^{2} (x)) x^{5}

Popular Examples

limit as x approaches-5-of 8/((-5)+5)

x \to - 5 - lim (\frac{8}{( - 5 ) + 5})

derivative of (3x-1^5)

\frac{d}{d x} ((3 x - 1)^{5})

integral of 1/(x^2y)

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

tangent of-x^3+9x^2-6x+9 tangent of

- x^{3} + 9 x^{2} - 6 x + 9

derivative of sin(2x)cos(3x)derivative of

sin (2 x) cos (3 x)

Frequently Asked Questions (FAQ)

What is the derivative of x^5sin(xtan(x)) ?
The derivative of x^5sin(xtan(x)) is 5x^4sin(x)tan(x)+sin(x)(1+sec^2(x))x^5
What is the first derivative of x^5sin(xtan(x)) ?
The first derivative of x^5sin(xtan(x)) is 5x^4sin(x)tan(x)+sin(x)(1+sec^2(x))x^5