What is the derivative of 5x^2cos(3x) ?

The derivative of 5x^2cos(3x) is 5(2xcos(3x)-3x^2sin(3x))

What is the first derivative of 5x^2cos(3x) ?

The first derivative of 5x^2cos(3x) is 5(2xcos(3x)-3x^2sin(3x))

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derivative of

5 x^{2} cos (3 x)

5 (2 x cos (3 x) - 3 x^{2} sin (3 x))

Solution steps

\frac{d}{d x} (5 x^{2} cos (3 x))

Take the constant out:

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

= 5 \frac{d}{d x} (x^{2} cos (3 x))

Apply the Product Rule:

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

f = x^{2}, g = cos (3 x)

= 5 (\frac{d}{d x} (x^{2}) cos (3 x) + \frac{d}{d x} (cos (3 x)) x^{2})

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

\frac{d}{d x} (cos (3 x)) = - sin (3 x) \cdot 3

= 5 (2 x cos (3 x) + (- sin (3 x) \cdot 3) x^{2})

Simplify

= 5 (2 x cos (3 x) - 3 x^{2} sin (3 x))

y^{^{''}} - \frac{7}{t} y^{^{'}} + \frac{32}{t ^{2}} y = 0

x^{2} \cdot y^{^{'}} - 4 x y = sin (3 x) \cdot x^{6}

x \to 0 lim (\frac{sin ( x ^{5} )}{x})

\int \frac{1}{1 + 9 x ^{2}} d x

\frac{- 3 e ^{(- s 2)}}{( s ^{2} - 5 s + 6 )}

What is the derivative of 5x^2cos(3x) ?
The derivative of 5x^2cos(3x) is 5(2xcos(3x)-3x^2sin(3x))
What is the first derivative of 5x^2cos(3x) ?
The first derivative of 5x^2cos(3x) is 5(2xcos(3x)-3x^2sin(3x))