6. Find the derivatives of the functions w.r.t. x from first principles: i) ex or e to the power x ii) esinx or e to the power sinx

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(i)

- x

(i i)

(- x)^{- 1}

(i i i)

sin (x + 1)

(i v)

cos (x - \frac{π}{8})

sin x

x

Differentiate each the following from first principles :

$(i) e^{- x}$

$(i i) e^{3 x}$

$(i i i) e^{a x + b}$

$(i v) x e^{x}$

$(v) x^{2} e^{x}$

$(v i) e^{x^{2} + 1}$

$(v i i) e^{\sqrt{2 x}}$

$(v i i i) e^{\sqrt{a x + b}}$

$(i x) a^{\sqrt{x}}$

$(x) 3^{x^{2}}$

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6. Find the derivatives of the functions w.r.t. x from first principles: i) e*x or e to the power x ii) e*sinx or e to the power sinx