What is the derivative of sin(x*x^2) ?

The derivative of sin(x*x^2) is cos(x)x^2+2xsin(x)

What is the first derivative of sin(x*x^2) ?

The first derivative of sin(x*x^2) is cos(x)x^2+2xsin(x)

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

cos (x) x^{2} + 2 x sin (x)

Solution steps

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

Apply the Product Rule:

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

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

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

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

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

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

x \to 2 lim (cos (\frac{π}{2} x))

\int \frac{1}{x + x ^{3}} d x

\int 3 (2 x - 1) (ln (x - 2)) d x

\frac{d}{d x} ((3 x + 1)^{- 1})

f (x) = \frac{- 5 x}{1 - x}

What is the derivative of sin(x*x^2) ?
The derivative of sin(x*x^2) is cos(x)x^2+2xsin(x)
What is the first derivative of sin(x*x^2) ?
The first derivative of sin(x*x^2) is cos(x)x^2+2xsin(x)