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

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

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

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

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

2 x cos (2 x^{2})

Solution steps

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

Apply the Product Rule:

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

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

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

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

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

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

Simplify

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

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

6 e^{- 5 t} \cdot cos (t)

n = 1 \sum \infty 5 (- \frac{1}{5})^{n}

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

x \to 0 + lim (ln (x) \cdot ln (1 + x))

4 x^{\frac{5}{4}} + 8 x^{\frac{3}{2}} + 9 x

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