What is the derivative of 4x^3+x+5sin(x) ?

The derivative of 4x^3+x+5sin(x) is 12x^2+1+5cos(x)

What is the first derivative of 4x^3+x+5sin(x) ?

The first derivative of 4x^3+x+5sin(x) is 12x^2+1+5cos(x)

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\frac{d}{d x} (4 x^{3} + x + 5 sin (x))

12 x^{2} + 1 + 5 cos (x)

Solution steps

\frac{d}{d x} (4 x^{3} + x + 5 sin (x))

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{d}{d x} (4 x^{3}) + \frac{d x}{d x} + \frac{d}{d x} (5 sin (x))

\frac{d}{d x} (4 x^{3}) = 12 x^{2}

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

\frac{d}{d x} (5 sin (x)) = 5 cos (x)

= 12 x^{2} + 1 + 5 cos (x)

What is the derivative of 4x^3+x+5sin(x) ?
The derivative of 4x^3+x+5sin(x) is 12x^2+1+5cos(x)
What is the first derivative of 4x^3+x+5sin(x) ?
The first derivative of 4x^3+x+5sin(x) is 12x^2+1+5cos(x)