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(1) Find the gradient using differentiation (2) If the gradient at (x₁,y₁) is m,y - y₁ = m(x - x₁)
(1) We differentiate the given equation:dy/dx = 2x + 3 <...

To answer this we will use implicit differentiation with respect to x. So start by differentiating each term. On the left hand side 0 differentiates to 0. On the right hand side 5x² differentia...

Since f(x) is a product of the two functions e^x and sin(x^2), we can use the product rule which states that if f(x)=g(x)h(x), then f'(x)=g'(x)h(x)+g(x)h'(x). Let g(x)=e^x and h(x)=sin(x^2). Since the dif...

ln is the natural log. The thing to remember with differentiating natural log is the simple formula U'/U. The U is whatever is in the brackets. This means we differentiate X^2 and divide it by X^2. X^2 ...

To differentiate y, we must used the product rule.The product rule is d/dx [f(x)g(x)] = f'(x)g(x) + g'(x)f(x)So here, we let f(x)= x^3 and g(x)= sin(x)Then, f'(x)= 3x^2 and g'(x) = cos(x)Then substituting...