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You can split the derivative into 2 parts: dx/dy (x^2*e^x) + dx/dy (x) For the first part you have to use the product rule, so let U=x^2 V=e^x U'=2x V'=Chain rule V'=dx/dy(e^x) dx/dy(x)=e^x 1=e^x Returning t...

The first thing we want to do is re-write the curve f(x) in a format in which we can read and easily plot a graph. If we can include the '3x' in the factorised part of the equation, it will be neater and we'...

In order to find the gradient of the curve at (1,1), we must first differentiate the equation of the curve. To do this, multiply the coefficient of x by the power of that same x. Then subtract one from the p...

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The tangent is the straight line passing through x=1, touching the curve only at that point. For x=1, y=(4+1)^3=125 Using the chain rule we obtain dy/dx = 3 8x (4x^2+1)^2. To then get the gradient of the tan...