The calculator will find the derivative of
x3+5x2+7x+4, with steps shown.
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Solution
The derivative of a sum/difference is the sum/difference of derivatives:
(dxd(x3+5x2+7x+4))=(dxd(x3)+dxd(5x2)+dxd(7x)+dxd(4))Apply the power rule dxd(xn)=nxn−1 with n=3:
(dxd(x3))+dxd(4)+dxd(7x)+dxd(5x2)=(3x2)+dxd(4)+dxd(7x)+dxd(5x2)The derivative of a constant is 0:
3x2+(dxd(4))+dxd(7x)+dxd(5x2)=3x2+(0)+dxd(7x)+dxd(5x2)Apply the constant multiple rule dxd(cf(x))=cdxd(f(x)) with c=5 and f(x)=x2:
3x2+(dxd(5x2))+dxd(7x)=3x2+(5dxd(x2))+dxd(7x)Apply the power rule dxd(xn)=nxn−1 with n=2:
3x2+5(dxd(x2))+dxd(7x)=3x2+5(2x)+dxd(7x)Apply the constant multiple rule dxd(cf(x))=cdxd(f(x)) with c=7 and f(x)=x:
3x2+10x+(dxd(7x))=3x2+10x+(7dxd(x))Apply the power rule dxd(xn)=nxn−1 with n=1, in other words, dxd(x)=1:
3x2+10x+7(dxd(x))=3x2+10x+7(1)Simplify:
3x2+10x+7=(x+1)(3x+7)Thus, dxd(x3+5x2+7x+4)=(x+1)(3x+7).
Answer
dxd(x3+5x2+7x+4)=(x+1)(3x+7)A