What is the derivative of 5*sin^2(x)-8*cos^5(x) ?

The derivative of 5*sin^2(x)-8*cos^5(x) is 5sin(2x)+40cos^4(x)sin(x)

What is the first derivative of 5*sin^2(x)-8*cos^5(x) ?

The first derivative of 5*sin^2(x)-8*cos^5(x) is 5sin(2x)+40cos^4(x)sin(x)

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derivative

5 sin (2 x) + 40 cos^{4} (x) sin (x)

Solution steps

\frac{d}{d x} (5 sin^{2} (x) - 8 cos^{5} (x))

Apply the Sum/Difference Rule:

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

= \frac{d}{d x} (5 sin^{2} (x)) - \frac{d}{d x} (8 cos^{5} (x))

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

\frac{d}{d x} (8 cos^{5} (x)) = - 40 cos^{4} (x) sin (x)

= 5 sin (2 x) - (- 40 cos^{4} (x) sin (x))

Simplify

= 5 sin (2 x) + 40 cos^{4} (x) sin (x)

What is the derivative of 5*sin^2(x)-8*cos^5(x) ?
The derivative of 5*sin^2(x)-8*cos^5(x) is 5sin(2x)+40cos^4(x)sin(x)
What is the first derivative of 5*sin^2(x)-8*cos^5(x) ?
The first derivative of 5*sin^2(x)-8*cos^5(x) is 5sin(2x)+40cos^4(x)sin(x)