en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular Calculus >

taylor φ^5cos(φ^2)

Solution

taylor

φ^{5} cos (φ^{2})

Solution

φ^{5} - \frac{1}{2} φ^{9} + \dots

Solution steps

Apply the Taylor Formula

= 0 + \frac{\frac{d}{d φ} ( φ ^{5} cos ( φ ^{2} ) ) ( 0 )}{1 !} φ + \frac{\frac{d ^{2}}{d φ ^{2}} ( φ ^{5} cos ( φ ^{2} ) ) ( 0 )}{2 !} φ^{2} + \frac{\frac{d ^{3}}{d φ ^{3}} ( φ ^{5} cos ( φ ^{2} ) ) ( 0 )}{3 !} φ^{3} + \dots

Evaluate Derivatives

= 0 + \frac{0}{1 !} φ + \frac{0}{2 !} φ^{2} + \frac{0}{3 !} φ^{3} + \frac{0}{4 !} φ^{4} + \frac{120}{5 !} φ^{5} + \frac{0}{6 !} φ^{6} + \frac{0}{7 !} φ^{7} + \frac{0}{8 !} φ^{8} + \frac{- 181440}{9 !} φ^{9} + \frac{0}{10 !} φ^{10} + \dots

Refine

= φ^{5} - \frac{1}{2} φ^{9} + \dots

Popular Examples

derivative of (2(x+8(x-6))/(x^2-7^2))

integral of (5sin(sqrt(x)))/(sqrt(x))

laplacetransform t*cos(pi*t)

laplacetransform e^{-3t}*sin(t)

Frequently Asked Questions (FAQ)

What is taylor φ^5cos(φ^2) ?
The answer to taylor φ^5cos(φ^2) is φ^5-1/2 φ^9+\ldots