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How would I differentiate y=2(e^x)sin(5x) ?

We can see that we have the product of two different functions, and so we need to use the product rule. We will separate the function and label each part u and v for clarity. So we let u = 2e^x...

Answered by Scott P. • Maths tutor

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theta = arctan(5x/2). Using implicit differentiation, find d theta/dx.

First, we must rearrange to give 2tan(θ) = 5x. Differentiate both sides with respect to x: 2sec²(θ)dθ/dx = 5 Use identity sin²(θ) + cos²(θ) = 1, dividing through by cos

Answered by Callum W. • Maths tutor

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f(x) = x^3 + 3x^2 + 5. Find f'(x) and f''(x).

With differentitaion you multiply the fatcor it's raised by and minus one from the order

e.g. y = x^n so y' = nx^(n-1)

So f'(x) = 3x^2 + 6x and f''(x) = 6x + 6

Answered by Nikita S. • Maths tutor

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What is the equation of the tangent to the circle (x-5)^2+(y-3)^2=9 at the points of intersection of the circle with the line 2x-y-1=0

Teh points of intersection can be found by subbing in y=2x-1 to the equation of the circle. (x-5)²+(2x-1-3)²=5x²-26x+33=9 so we have 5x²-26x+24=0. Solving the q...

Answered by Tutor67416 D. • Maths tutor

2836 Views

When do I use the product rule as opposed to the chain rule?

The product rule is used when two functions of x are multiplied by each other, hence, product. So this can be used to differnetiatate 3x²* x+1 or more complex functions like sinxcosx.

Th...

Answered by Lota U. • Maths tutor

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