What is the derivative of f(x)=-10xsin(5x^2+5) ?

The derivative of f(x)=-10xsin(5x^2+5) is -10(sin(5x^2+5)+10x^2cos(5x^2+5))

What is the first derivative of f(x)=-10xsin(5x^2+5) ?

The first derivative of f(x)=-10xsin(5x^2+5) is -10(sin(5x^2+5)+10x^2cos(5x^2+5))

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derivative of

f (x) = - 10 x sin (5 x^{2} + 5)

- 10 (sin (5 x^{2} + 5) + 10 x^{2} cos (5 x^{2} + 5))

Solution steps

\frac{d}{d x} (- 10 x sin (5 x^{2} + 5))

Take the constant out:

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

= - 10 \frac{d}{d x} (x sin (5 x^{2} + 5))

Apply the Product Rule:

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

f = x, g = sin (5 x^{2} + 5)

= - 10 (\frac{d x}{d x} sin (5 x^{2} + 5) + \frac{d}{d x} (sin (5 x^{2} + 5)) x)

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

\frac{d}{d x} (sin (5 x^{2} + 5)) = cos (5 x^{2} + 5) \cdot 10 x

= - 10 (1 \cdot sin (5 x^{2} + 5) + cos (5 x^{2} + 5) \cdot 10 xx)

Simplify

- 10 (1 \cdot sin (5 x^{2} + 5) + cos (5 x^{2} + 5) \cdot 10 xx) : - 10 (sin (5 x^{2} + 5) + 10 x^{2} cos (5 x^{2} + 5))

= - 10 (sin (5 x^{2} + 5) + 10 x^{2} cos (5 x^{2} + 5))

What is the derivative of f(x)=-10xsin(5x^2+5) ?
The derivative of f(x)=-10xsin(5x^2+5) is -10(sin(5x^2+5)+10x^2cos(5x^2+5))
What is the first derivative of f(x)=-10xsin(5x^2+5) ?
The first derivative of f(x)=-10xsin(5x^2+5) is -10(sin(5x^2+5)+10x^2cos(5x^2+5))