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Find the equation of the tangent to the curve y = 3x^2(x+2)^6 at the point (-1,3), in the form y = mx+c

Curve: y = 3x²(x+2)⁶Coordinate: (-1, 3)

This is typically a C3/4 level question because of the differentiation, but the rest of t...

Answered by BUNEME K. • Maths tutor

11767 Views

Integrate sin(x)cos(x)^2 from 0 to π/2

Use substitution u=cos(x) resulting in du=-sin(x)dx: ∫₀^π/2sin(x)cos(x)^2dx = ∫₀^π/2-u^2du = [-1/3 u^3]_x=0^x=π/2 = [-1/3 cos(x)^3]₀

Answered by Benedek S. • Maths tutor

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If y = exp(x^2), find dy/dx

Recall that the derivative of exp(x) is exp(x), but notice this question is slightly more complex due to the x^2 term. This is example of differentiationg composite functions, and so the chain rule is req...

Answered by Stuart B. • Maths tutor

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Why does sin^2(x)+cos^2(x)=1?

We can understand this identity in two different, useful ways.

Firstly, we can use Euler's identities from trigonometry to obtain the desired result using straightforward algebra. We know that:

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Answered by Alex M. • Maths tutor

3564 Views

Derive Law of Cosines using Pythagorean Theorem

Consider the triangle ABC. Denote h the altitude through B and D the point where h intersects the (extended) base AC
Cosine function for triangle ADB.

cos α= x/c => x=c*cos α

...

Answered by Jan M. • Maths tutor

3085 Views