differentiate x^3(1+x)^5 with respect for x
First we have to use the product rule, remember that if we have h(x)=f(x)g(x) then h'(x)=f'(x)g(x)+f(x)g'(x).So h'(x) = x^3D[(x+1)^5]+(x+1)^5D[x^3]Completing the unfinished derivatives,h'(x) = x^3[5(x+1)^4]+(x+1)^5[3x^2]Simplifies to.h'(x) = 5x^3(x+1)^4+3x^2(x+1)^5remember that we do the (x+1)^5 in the standard way.
RL
Related Maths GCSE answers
All answers ▸4x^2 + 8x + 3 can be written in the form a(x + b)^2 + c where a, b and c are whole numbers. Work out the values of a, b and c.
A square, with sides of length x cm, is inside a circle. Each vertex of the square is on the circumference of the circle. The area of the circle is 49 cm^2. Work out the value of x. Give your answer correct to 3 significant figures.
The perimeter of a right-angled triangle is 72 cm. The lengths of its sides are in the ratio 3 : 4 : 5 Work out the area of the triangle.
Paul travels from Rye to Eston at an average speed of 90 km/h. He travels for T hours. Mary makes the same journey at an average speed of 70 km/h. She travels for 1 hour longer than Paul. Work out the value of T