Sue Pemberton, Julianne Hughes and, Julian Gilbey Solutions for Chapter: Differentiation, Exercise 2: EXERCISE 4A

Use the product rule to differentiate the following with respect to $x :$

$\left(2x-5\right){\left(3x^2+1\right)}^2$

Find the gradient of the curve $y=x^2\sqrt{x+4}$ at the point $(-3, 9).$

Find the equation of the tangent to the curve $y=(2-x{)}^3(x+1{)}^4$ at the point where $x=1.$

Find the gradient of the tangent to the curve $y=(x+2)(x-1{)}^3$ at the point where the curve meets the $y$-axis.

Find the $x$-coordinate of the points on the curve $y=(3-x{)}^3(x+1{)}^2$ where the gradient is zero.

Find the $x$-coordinate of the point on the curve $y=(x+2)\sqrt{1-2x}$ where the gradient is zero.

Sketch the curve $y=(x-1{)}^2(5-2x)+3.$

The curve $y=(x-1{)}^2(5-2x)+3$ has stationary points at $A$ and $B.$ The straight line through $A$ and $B$ cuts the axes at $P$ and $Q.$ Find the area of the triangle $POQ.$