en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

derivative of sin(x^{tan(x}))

Solution

\frac{d}{d x} (sin (x^{t a n (x)}))

Solution

x^{t a n (x)} cos (x^{t a n (x)}) (sec^{2} (x) ln (x) + \frac{tan ( x )}{x})

Solution steps

\frac{d}{d x} (sin (x^{t a n (x)}))

Apply the chain rule:

cos (x^{t a n (x)}) \frac{d}{d x} (x^{t a n (x)})

= cos (x^{t a n (x)}) \frac{d}{d x} (x^{t a n (x)})

\frac{d}{d x} (x^{t a n (x)}) = e^{t a n (x) l n (x)} (sec^{2} (x) ln (x) + \frac{tan ( x )}{x})

= cos (x^{t a n (x)}) e^{t a n (x) l n (x)} (sec^{2} (x) ln (x) + \frac{tan ( x )}{x})

e^{t a n (x) l n (x)} = x^{t a n (x)}

= x^{t a n (x)} cos (x^{t a n (x)}) (sec^{2} (x) ln (x) + \frac{tan ( x )}{x})

Popular Examples

(2x+1)y^'+2y=4x,y(0)=1

(2 x + 1) y^{^{'}} + 2 y = 4 x, y (0) = 1

(\partial)/(\partial z)(ln(x^2+y^4)-z)

\frac{\partial}{\partial z} (ln (x^{2} + y^{4}) - z)

25y^{''}-y=xe^{x/5},y(0)=1,y^'(0)=0

25 y^{^{''}} - y = x e^{\frac{x}{5}}, y (0) = 1, y^{^{'}} (0) = 0

limit as x approaches infinity of 1/(x(ln(x))^4)

x \to \infty lim (\frac{1}{x ( ln ( x ) ) ^{4}})

integral from 1 to 3 of sqrt(1+(x^3-1/(4x^3))^2)

\int_{1}^{3} 1 + (x^{3} - \frac{1}{4 x ^{3}})^{2} d x

Frequently Asked Questions (FAQ)

What is the derivative of sin(x^{tan(x})) ?
The derivative of sin(x^{tan(x})) is x^{tan(x)}cos(x^{tan(x)})(sec^2(x)ln(x)+(tan(x))/x)
What is the first derivative of sin(x^{tan(x})) ?
The first derivative of sin(x^{tan(x})) is x^{tan(x)}cos(x^{tan(x)})(sec^2(x)ln(x)+(tan(x))/x)