What is the derivative of (sin^5(x)/5-(sin^7(x))/7) ?

The derivative of (sin^5(x)/5-(sin^7(x))/7) is sin^4(x)cos^3(x)

What is the first derivative of (sin^5(x)/5-(sin^7(x))/7) ?

The first derivative of (sin^5(x)/5-(sin^7(x))/7) is sin^4(x)cos^3(x)

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\frac{d}{d x} (\frac{sin ^{5} ( x )}{5} - \frac{sin ^{7} ( x )}{7})

sin^{4} (x) cos^{3} (x)

Solution steps

\frac{d}{d x} (\frac{sin ^{5} ( x )}{5} - \frac{sin ^{7} ( x )}{7})

Apply the Sum/Difference Rule:

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

= \frac{d}{d x} (\frac{sin ^{5} ( x )}{5}) - \frac{d}{d x} (\frac{sin ^{7} ( x )}{7})

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

\frac{d}{d x} (\frac{sin ^{7} ( x )}{7}) = sin^{6} (x) cos (x)

= sin^{4} (x) cos (x) - sin^{6} (x) cos (x)

Simplify

sin^{4} (x) cos (x) - sin^{6} (x) cos (x) : sin^{4} (x) cos^{3} (x)

= sin^{4} (x) cos^{3} (x)

\frac{d}{d x} (e^{x} - cos (x))

y = (2 x + 1) (x + 5)^{3}

n = 0 \sum \infty (- 1)^{n} (2^{n})

\frac{d}{d x} (- \frac{1}{3 x ^{3}})

y = 30 e^{- 0.0000323 (1600)}

What is the derivative of (sin^5(x)/5-(sin^7(x))/7) ?
The derivative of (sin^5(x)/5-(sin^7(x))/7) is sin^4(x)cos^3(x)
What is the first derivative of (sin^5(x)/5-(sin^7(x))/7) ?
The first derivative of (sin^5(x)/5-(sin^7(x))/7) is sin^4(x)cos^3(x)