What is the tangent of 6-5x^3 ?

The tangent of 6-5x^3 is y=-15a_{0}^2x+6+10a_{0}^3

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tangent of 6-5x^3

tangent of

6 - 5 x^{3}

y = - 15 a_{0}^{2} x + 6 + 10 a_{0}^{3}

Solution steps

Compute the tangent line to the general point

x = a_{0}

Find the tangent point:

(a_{0}, 6 - 5 a_{0}^{3})

Find the slope of

y = 6 - 5 x^{3} : \frac{d y}{d x} = - 15 x^{2}

Compute the slope of

y = 6 - 5 x^{3}

x = a_{0} : m = - 15 a_{0}^{2}

Find the line with slope m=

- 15 a_{0}^{2}

and passing through

(a_{0}, 6 - 5 a_{0}^{3}) : y = - 15 a_{0}^{2} x + 6 + 10 a_{0}^{3}

y = - 15 a_{0}^{2} x + 6 + 10 a_{0}^{3}

6 x^{2} y^{2} d x + 4 x^{3} y d y = 0

y = 5 x, x = 5, y = \frac{5}{x}, x = 0

\int tan^{2} (5 x) d x

\int \frac{3}{x ( ln ( 3 x ) ) ^{2}} d x

y = (8 x + 5)^{3}

What is the tangent of 6-5x^3 ?
The tangent of 6-5x^3 is y=-15a_{0}^2x+6+10a_{0}^3