What is the derivative of (d^2/(dx^2)(x^4)+cos(x)+1) ?

The derivative of (d^2/(dx^2)(x^4)+cos(x)+1) is 24x+sin(x)

What is the first derivative of (d^2/(dx^2)(x^4)+cos(x)+1) ?

The first derivative of (d^2/(dx^2)(x^4)+cos(x)+1) is 24x+sin(x)

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\frac{d}{d x} (\frac{d ^{2}}{d x ^{2}} (x^{4}) + cos (x) + 1)

24 x + sin (x)

Solution steps

\frac{d}{d x} (\frac{d ^{2}}{d x ^{2}} (x^{4}) + cos (x) + 1)

Apply the Sum/Difference Rule:

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

= \frac{d}{d x} (\frac{d ^{2}}{d x ^{2}} (x^{4})) + \frac{d}{d x} (cos (x)) + \frac{d}{d x} (1)

\frac{d}{d x} (\frac{d ^{2}}{d x ^{2}} (x^{4})) = 24 x

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

\frac{d ^{3}}{d x ^{3}} (cos (x)) = sin (x)

\frac{d ^{3}}{d x ^{3}} (1) = 0

= 24 x + sin (x) + 0

Simplify

= 24 x + sin (x)

What is the derivative of (d^2/(dx^2)(x^4)+cos(x)+1) ?
The derivative of (d^2/(dx^2)(x^4)+cos(x)+1) is 24x+sin(x)
What is the first derivative of (d^2/(dx^2)(x^4)+cos(x)+1) ?
The first derivative of (d^2/(dx^2)(x^4)+cos(x)+1) is 24x+sin(x)