What is the derivative of e^{-(x+2)}-sin(x^2)+1 ?

The derivative of e^{-(x+2)}-sin(x^2)+1 is -2xcos(x^2)-e^{-x-2}

What is the first derivative of e^{-(x+2)}-sin(x^2)+1 ?

The first derivative of e^{-(x+2)}-sin(x^2)+1 is -2xcos(x^2)-e^{-x-2}

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derivative of

e^{- (x + 2)} - sin (x^{2}) + 1

- 2 x cos (x^{2}) - e^{- x - 2}

Solution steps

\frac{d}{d x} (e^{- (x + 2)} - sin (x^{2}) + 1)

Simplify

e^{- (x + 2)} - sin (x^{2}) + 1 : e^{- x - 2} - sin (x^{2}) + 1

= \frac{d}{d x} (e^{- x - 2} - sin (x^{2}) + 1)

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{d}{d x} (e^{- x - 2}) - \frac{d}{d x} (sin (x^{2})) + \frac{d}{d x} (1)

\frac{d}{d x} (e^{- x - 2}) = - e^{- x - 2}

\frac{d}{d x} (sin (x^{2})) = cos (x^{2}) \cdot 2 x

\frac{d}{d x} (1) = 0

= - e^{- x - 2} - cos (x^{2}) \cdot 2 x + 0

Simplify

= - 2 x cos (x^{2}) - e^{- x - 2}

\frac{x ^{2}}{4} + x + 1

\int \frac{1}{sin ( x ) - 2 csc ( x )} d x

y = \frac{5 x}{x - 2}, (3, 15)

f (x) = \frac{x ^{2}}{x + 4}

\int (6 e^{x}) d x

What is the derivative of e^{-(x+2)}-sin(x^2)+1 ?
The derivative of e^{-(x+2)}-sin(x^2)+1 is -2xcos(x^2)-e^{-x-2}
What is the first derivative of e^{-(x+2)}-sin(x^2)+1 ?
The first derivative of e^{-(x+2)}-sin(x^2)+1 is -2xcos(x^2)-e^{-x-2}