What is the tangent of y=8x^2-5x^{11} ?

The tangent of y=8x^2-5x^{11} is y=(16a_{0}-55a_{0}^{10})x+50a_{0}^{11}-8a_{0}^2

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tangent of y=8x^2-5x^{11}

tangent of

y = 8 x^{2} - 5 x^{11}

y = (16 a_{0} - 55 a_{0}^{10}) x + 50 a_{0}^{11} - 8 a_{0}^{2}

Solution steps

Compute the tangent line to the general point

x = a_{0}

Find the tangent point:

(a_{0}, 8 a_{0}^{2} - 5 a_{0}^{11})

Find the slope of

y = 8 x^{2} - 5 x^{11} : \frac{d y}{d x} = 16 x - 55 x^{10}

Compute the slope of

y = 8 x^{2} - 5 x^{11}

x = a_{0} : m = 16 a_{0} - 55 a_{0}^{10}

Find the line with slope m=

16 a_{0} - 55 a_{0}^{10}

and passing through

(a_{0}, 8 a_{0}^{2} - 5 a_{0}^{11}) : y = (16 a_{0} - 55 a_{0}^{10}) x + 50 a_{0}^{11} - 8 a_{0}^{2}

y = (16 a_{0} - 55 a_{0}^{10}) x + 50 a_{0}^{11} - 8 a_{0}^{2}

\int (x - 2) e^{x + 3} d x

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

y = \frac{x}{3}, y = x - 2

\frac{d}{d x} (2 x^{2} + 4 x + 5)

e^{x + 3 y} d y = x d x

What is the tangent of y=8x^2-5x^{11} ?
The tangent of y=8x^2-5x^{11} is y=(16a_{0}-55a_{0}^{10})x+50a_{0}^{11}-8a_{0}^2