What is the derivative of 3+t^5+sin(pit) ?

The derivative of 3+t^5+sin(pit) is 5t^4+picos(pit)

What is the first derivative of 3+t^5+sin(pit) ?

The first derivative of 3+t^5+sin(pit) is 5t^4+picos(pit)

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derivative of

3 + t^{5} + sin (π t)

5 t^{4} + π cos (π t)

Solution steps

\frac{d}{d t} (3 + t^{5} + sin (π t))

Apply the Sum/Difference Rule:

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

= \frac{d}{d t} (3) + \frac{d}{d t} (t^{5}) + \frac{d}{d t} (sin (π t))

\frac{d}{d t} (3) = 0

\frac{d}{d t} (t^{5}) = 5 t^{4}

\frac{d}{d t} (sin (π t)) = cos (π t) π

= 0 + 5 t^{4} + cos (π t) π

Simplify

= 5 t^{4} + π cos (π t)

\frac{d y}{d x} = \frac{y}{x} - cos (\frac{y}{x})

\int (x^{4} - 6 x) d x

\int \frac{sin ( 20 x )}{1 + cos ^{2} ( 20 x )} d x

2 y^{^{''}} + 35 y = 0, y (0) = 9, y^{^{'}} (0) = 6

What is the derivative of 3+t^5+sin(pit) ?
The derivative of 3+t^5+sin(pit) is 5t^4+picos(pit)
What is the first derivative of 3+t^5+sin(pit) ?
The first derivative of 3+t^5+sin(pit) is 5t^4+picos(pit)