What is the derivative of 7xsin(x^2) ?

The derivative of 7xsin(x^2) is 7(sin(x^2)+2x^2cos(x^2))

What is the first derivative of 7xsin(x^2) ?

The first derivative of 7xsin(x^2) is 7(sin(x^2)+2x^2cos(x^2))

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derivative of

7 x sin (x^{2})

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

Solution steps

\frac{d}{d x} (7 x sin (x^{2}))

Take the constant out:

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

= 7 \frac{d}{d x} (x sin (x^{2}))

Apply the Product Rule:

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

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

= 7 (\frac{d x}{d x} sin (x^{2}) + \frac{d}{d x} (sin (x^{2})) x)

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

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

= 7 (1 \cdot sin (x^{2}) + cos (x^{2}) \cdot 2 xx)

Simplify

7 (1 \cdot sin (x^{2}) + cos (x^{2}) \cdot 2 xx) : 7 (sin (x^{2}) + 2 x^{2} cos (x^{2}))

= 7 (sin (x^{2}) + 2 x^{2} cos (x^{2}))

\int - cos (x) + sin (x) + 4 d x

\int \frac{csc ^{2} ( x )}{cot ( x ) + 1} d x

f (x) = (2 + 5 x) (5 - 4 x), at x = 1

y^{^{'}} - y = 5.2

\int sin (3 z) cos (2) (3 z) d z

What is the derivative of 7xsin(x^2) ?
The derivative of 7xsin(x^2) is 7(sin(x^2)+2x^2cos(x^2))
What is the first derivative of 7xsin(x^2) ?
The first derivative of 7xsin(x^2) is 7(sin(x^2)+2x^2cos(x^2))