What is the derivative of 9xcos(x^2) ?

The derivative of 9xcos(x^2) is 9(cos(x^2)-2x^2sin(x^2))

What is the first derivative of 9xcos(x^2) ?

The first derivative of 9xcos(x^2) is 9(cos(x^2)-2x^2sin(x^2))

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derivative of

9 x cos (x^{2})

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

Solution steps

\frac{d}{d x} (9 x cos (x^{2}))

Take the constant out:

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

= 9 \frac{d}{d x} (x cos (x^{2}))

Apply the Product Rule:

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

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

= 9 (\frac{d x}{d x} cos (x^{2}) + \frac{d}{d x} (cos (x^{2})) x)

\frac{d x}{d x} = 1

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

= 9 (1 \cdot cos (x^{2}) + (- sin (x^{2}) \cdot 2 x) x)

Simplify

9 (1 \cdot cos (x^{2}) + (- sin (x^{2}) \cdot 2 x) x) : 9 (cos (x^{2}) - 2 x^{2} sin (x^{2}))

= 9 (cos (x^{2}) - 2 x^{2} sin (x^{2}))

x \to - \infty lim (6^{x})

y^{^{'}} - 3 y = e^{x}

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

f (x) = 4 - x^{2}, at x = 2

\int cos (\frac{1}{2} x) d x

What is the derivative of 9xcos(x^2) ?
The derivative of 9xcos(x^2) is 9(cos(x^2)-2x^2sin(x^2))
What is the first derivative of 9xcos(x^2) ?
The first derivative of 9xcos(x^2) is 9(cos(x^2)-2x^2sin(x^2))