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Popular >

taylor f(x)=cos(x^4)

Solution

taylor

f (x) = cos (x^{4})

Solution

1 - \frac{1}{2} x^{8} + \dots

Solution steps

Apply the Taylor Formula

= 1 + \frac{\frac{d}{d x} ( cos ( x ^{4} ) ) ( 0 )}{1 !} x + \frac{\frac{d ^{2}}{d x ^{2}} ( cos ( x ^{4} ) ) ( 0 )}{2 !} x^{2} + \frac{\frac{d ^{3}}{d x ^{3}} ( cos ( x ^{4} ) ) ( 0 )}{3 !} x^{3} + \dots

Evaluate Derivatives

= 1 + \frac{0}{1 !} x + \frac{0}{2 !} x^{2} + \frac{0}{3 !} x^{3} + \frac{0}{4 !} x^{4} + \frac{0}{5 !} x^{5} + \frac{0}{6 !} x^{6} + \frac{0}{7 !} x^{7} + \frac{- 20160}{8 !} x^{8} + \frac{0}{9 !} x^{9} + \frac{0}{10 !} x^{10} + \dots

Refine

= 1 - \frac{1}{2} x^{8} + \dots

Popular Examples

derivative of y=t derivative of

y = t

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x \to 0 lim (sin^{5} (2 x^{2}))

derivative of x^3-3x+6

\frac{d}{d x} (x^{3} - 3 x + 6)

derivative of e^{-2x+1}

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

derivative of g(t)= 3/(sqrt(t))derivative of

g (t) = \frac{3}{t}

Frequently Asked Questions (FAQ)

What is taylor f(x)=cos(x^4) ?
The answer to taylor f(x)=cos(x^4) is 1-1/2 x^8+\ldots