What is the tangent of f(x)=(2x)/(e^{3x^2)},\at x=-1 ?

The tangent of f(x)=(2x)/(e^{3x^2)},\at x=-1 is y=-(10)/(e^3)x-(12)/(e^3)

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tangent of f(x)=(2x)/(e^{3x^2)},\at x=-1

tangent of

f (x) = \frac{2 x}{e ^{3 x^{2}}}, at x = - 1

y = - \frac{10}{e ^{3}} x - \frac{12}{e ^{3}}

Solution steps

Find the tangent point:

(- 1, - \frac{2}{e ^{3}})

Find the slope of

f (x) = \frac{2 x}{e ^{3 x^{2}}} : \frac{df ( x )}{d x} = \frac{2 ( 1 - 6 x ^{2} )}{e ^{3 x^{2}}}

EN : T i tl e G e n er a l Eq u a t i o n Sl o p e A t P o in t 2 Eq : m = - \frac{10}{e ^{3}}

Find the line with slope m=

- \frac{10}{e ^{3}}

and passing through

(- 1, - \frac{2}{e ^{3}}) : y = - \frac{10}{e ^{3}} x - \frac{12}{e ^{3}}

y = - \frac{10}{e ^{3}} x - \frac{12}{e ^{3}}

\int \frac{1}{2 + 3 y ^{2}} d y

\int - 2 x + 3 d x

\frac{d}{d x} (2 x + 2)

\int \frac{x}{e ^{- 2 x}} d x

\int \frac{1}{u ^{2} + 2} d u

What is the tangent of f(x)=(2x)/(e^{3x^2)},\at x=-1 ?
The tangent of f(x)=(2x)/(e^{3x^2)},\at x=-1 is y=-(10)/(e^3)x-(12)/(e^3)