What is the derivative of (3x^{-2}x)(e^x-sin(x)) ?

The derivative of (3x^{-2}x)(e^x-sin(x)) is (3(e^xx-xcos(x)-e^x+sin(x)))/(x^2)

What is the first derivative of (3x^{-2}x)(e^x-sin(x)) ?

The first derivative of (3x^{-2}x)(e^x-sin(x)) is (3(e^xx-xcos(x)-e^x+sin(x)))/(x^2)

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derivative of

(3 x^{- 2} x) (e^{x} - sin (x))

\frac{3 ( e ^{x} x - x cos ( x ) - e ^{x} + sin ( x ) )}{x ^{2}}

Solution steps

\frac{d}{d x} (3 x^{- 2} x (e^{x} - sin (x)))

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

= 3 \frac{d}{d x} (x^{- 2} x (e^{x} - sin (x)))

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = x^{- 2}, g = x (e^{x} - sin (x))

= 3 (\frac{d}{d x} (x^{- 2}) x (e^{x} - sin (x)) + \frac{d}{d x} (x (e^{x} - sin (x))) x^{- 2})

\frac{d}{d x} (x^{- 2}) = - \frac{2}{x ^{3}}

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

= 3 ((- \frac{2}{x ^{3}}) x (e^{x} - sin (x)) + (e^{x} - sin (x) + x (e^{x} - cos (x))) x^{- 2})

Simplify

3 ((- \frac{2}{x ^{3}}) x (e^{x} - sin (x)) + (e^{x} - sin (x) + x (e^{x} - cos (x))) x^{- 2}) : \frac{3 ( e ^{x} x - x cos ( x ) - e ^{x} + sin ( x ) )}{x ^{2}}

= \frac{3 ( e ^{x} x - x cos ( x ) - e ^{x} + sin ( x ) )}{x ^{2}}

\frac{2 - 2}{3 t}

4 x^{3} - x^{2} + 1^{2}

\frac{t ^{2}}{20} + \frac{t}{5}

\frac{sin ( x )}{( 1 + cos ( x ) )}

ln (t + 1) - t

What is the derivative of (3x^{-2}x)(e^x-sin(x)) ?
The derivative of (3x^{-2}x)(e^x-sin(x)) is (3(e^xx-xcos(x)-e^x+sin(x)))/(x^2)
What is the first derivative of (3x^{-2}x)(e^x-sin(x)) ?
The first derivative of (3x^{-2}x)(e^x-sin(x)) is (3(e^xx-xcos(x)-e^x+sin(x)))/(x^2)