What is the derivative of-4x^2cos(x) ?

The derivative of-4x^2cos(x) is -4(2xcos(x)-x^2sin(x))

What is the first derivative of-4x^2cos(x) ?

The first derivative of-4x^2cos(x) is -4(2xcos(x)-x^2sin(x))

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derivative of

- 4 x^{2} cos (x)

- 4 (2 x cos (x) - x^{2} sin (x))

Solution steps

\frac{d}{d x} (- 4 x^{2} cos (x))

Take the constant out:

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

= - 4 \frac{d}{d x} (x^{2} cos (x))

Apply the Product Rule:

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

f = x^{2}, g = cos (x)

= - 4 (\frac{d}{d x} (x^{2}) cos (x) + \frac{d}{d x} (cos (x)) x^{2})

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

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

= - 4 (2 x cos (x) + (- sin (x)) x^{2})

Simplify

= - 4 (2 x cos (x) - x^{2} sin (x))

\frac{lo g _{10} ( 1 )}{x ^{3}}

\frac{1}{( x ^{2} + 3 )}

\frac{1}{x lo g _{10} ( x )}

x^{3} - 3 x^{2}

sin (10 x) + cos (15 x)

What is the derivative of-4x^2cos(x) ?
The derivative of-4x^2cos(x) is -4(2xcos(x)-x^2sin(x))
What is the first derivative of-4x^2cos(x) ?
The first derivative of-4x^2cos(x) is -4(2xcos(x)-x^2sin(x))