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1. Set y=a^x2. Take the natural log of both sides: ln(y)=ln(a^x)3. Using the log rules, simplify: ln(y)=xln(a)4. Differentiate both sides with respect to x: 1/y dy/dx=lna+05. Rearrange: dy/dx=yln(a)6. ...

1. Differentiate the Equation of the curve to find the gradient: y'=3x^2

2. The gradient of the tangent is found by substituting x=1 into y'=3x^2: Gradient of tangent=3

3. N...

We are given the substitution to use, so the first step is to differentiate "u" with respect to x. 

du/dx = -sin(x)

Now, to replace the "dx&q...

As we are differentiating a product (two things times together) we can use the product rule which is if:

                       y = u(x)v(x)

then

             ...

When we integrate a function we must first raise the power of x in each term by one. The first term therefore becomes x^(5/2). The second term can be thought of as x^0 which we know that any number to ...