What is the tangent of x^4-2x^2+1 ?

The tangent of x^4-2x^2+1 is y=(4a_{0}^3-4a_{0})x-3a_{0}^4+2a_{0}^2+1

Popular >

tangent of x^4-2x^2+1

tangent of

x^{4} - 2 x^{2} + 1

y = (4 a_{0}^{3} - 4 a_{0}) x - 3 a_{0}^{4} + 2 a_{0}^{2} + 1

Solution steps

Compute the tangent line to the general point

x = a_{0}

Find the tangent point:

(a_{0}, a_{0}^{4} - 2 a_{0}^{2} + 1)

Find the slope of

y = x^{4} - 2 x^{2} + 1 : \frac{d y}{d x} = 4 x^{3} - 4 x

Compute the slope of

y = x^{4} - 2 x^{2} + 1

x = a_{0} : m = 4 a_{0}^{3} - 4 a_{0}

Find the line with slope m=

4 a_{0}^{3} - 4 a_{0}

and passing through

(a_{0}, a_{0}^{4} - 2 a_{0}^{2} + 1) : y = (4 a_{0}^{3} - 4 a_{0}) x - 3 a_{0}^{4} + 2 a_{0}^{2} + 1

y = (4 a_{0}^{3} - 4 a_{0}) x - 3 a_{0}^{4} + 2 a_{0}^{2} + 1

\frac{d}{d x} (2 e^{4 x} sin (π) x)

\frac{d}{d x} (e^{4^{x}})

n = 1 \sum \infty \frac{1}{( n ^{2} + 5 n )}

\int \frac{sin ( ln ( x ) ) cos ( 2 ln ( x ) )}{2 x} d x

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

What is the tangent of x^4-2x^2+1 ?
The tangent of x^4-2x^2+1 is y=(4a_{0}^3-4a_{0})x-3a_{0}^4+2a_{0}^2+1