How to Simplify the Derivative of a Cosine-Sine Product

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Homework Statement



Find the derivative:

F(x)= cos (x)* sin(5x^2 +7)

Homework Equations





The Attempt at a Solution



I used the power rule and the chain rule and wound up with this: but i don't know how to simplify it...

= -sin(x)*sin(5x^2+7)+(10x)*(cos x)*(cos (5x^2+7)
 
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n.a.s.h said:

Homework Statement



Find the derivative:

F(x)= cos (x)* sin(5x^2 +7)

Homework Equations





The Attempt at a Solution



I used the power rule and the chain rule and wound up with this: but i don't know how to simplify it...

= -sin(x)*sin(5x^2+7)+(10x)*(cos x)*(cos (5x^2+7)
You also used the product rule.

I don't see much that you can do to simplify this.
 
n.a.s.h said:

Homework Statement



Find the derivative:

F(x)= cos (x)* sin(5x^2 +7)

Homework Equations





The Attempt at a Solution



I used the power rule and the chain rule and wound up with this: but i don't know how to simplify it...

= -sin(x)*sin(5x^2+7)+(10x)*(cos x)*(cos (5x^2+7)

yeah sorry i meant product rule
 

Thread 'Prove that the integral is equal to ##\pi^2/8##'

Prove $$\int\limits_0^{\sqrt2/4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx = \frac{\pi^2}{8}.$$ Let $$I = \int\limits_0^{\sqrt 2 / 4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx. \tag{1}$$ The representation integral of ##\arcsin## is $$\arcsin u = \int\limits_{0}^{1} \frac{\mathrm dt}{\sqrt{1-t^2}}, \qquad 0 \leqslant u \leqslant 1.$$ Plugging identity above into ##(1)## with ##u...
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