What is the derivative of-sin(7x^2*14x) ?

The derivative of-sin(7x^2*14x) is -14(14x^2cos(7x^2)+sin(7x^2))

What is the first derivative of-sin(7x^2*14x) ?

The first derivative of-sin(7x^2*14x) is -14(14x^2cos(7x^2)+sin(7x^2))

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\frac{d}{d x} (- sin (7 x^{2}) \cdot 14 x)

- 14 (14 x^{2} cos (7 x^{2}) + sin (7 x^{2}))

Solution steps

\frac{d}{d x} (- sin (7 x^{2}) \cdot 14 x)

Take the constant out:

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

= - 14 \frac{d}{d x} (sin (7 x^{2}) x)

Apply the Product Rule:

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

f = sin (7 x^{2}), g = x

= - 14 (\frac{d}{d x} (sin (7 x^{2})) x + \frac{d x}{d x} sin (7 x^{2}))

\frac{d}{d x} (sin (7 x^{2})) = cos (7 x^{2}) \cdot 14 x

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

= - 14 (cos (7 x^{2}) \cdot 14 xx + 1 \cdot sin (7 x^{2}))

Simplify

- 14 (cos (7 x^{2}) \cdot 14 xx + 1 \cdot sin (7 x^{2})) : - 14 (14 x^{2} cos (7 x^{2}) + sin (7 x^{2}))

= - 14 (14 x^{2} cos (7 x^{2}) + sin (7 x^{2}))

\frac{d x}{d t} + 2 t x = t, x (0) = \frac{3}{2}

f (x) = 5 x^{3} + 4 x, at x = - 3

f (x) = x \cdot cos (x)

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

\frac{e ^{x}}{8 + e ^{x}}

What is the derivative of-sin(7x^2*14x) ?
The derivative of-sin(7x^2*14x) is -14(14x^2cos(7x^2)+sin(7x^2))
What is the first derivative of-sin(7x^2*14x) ?
The first derivative of-sin(7x^2*14x) is -14(14x^2cos(7x^2)+sin(7x^2))